MENSURATION

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Mensuration is the branch of mathematics which deals with the study of different geometrical shapes, their areas and Volume. In the broadest sense, it is all about the process of measurement. It is based on the use of algebraic equations and geometric calculations to provide measurement data regarding the width, depth and volume of a given object or group of objects

Pythagorean Theorem (Pythagoras’ theorem)

In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides

c² = a² + b² where c is the length of the hypotenuse and a and b are the lengths of the other two sides

Pi is a mathematical constant which is the ratio of a circle’s circumference to its diameter. It is denoted by π

π≈3.14≈227

Geometric Shapes and solids and Important Formulas

Geometric Shapes	Description	Formulas
	Rectangle l = Length b = Breadth d= Length of diagonal	Area = lb Perimeter = 2(l + b) d = √l2+b2
	Square a = Length of a side d= Length of diagonal	Area= aa=1/2dd* Perimeter = 4a d = 2√a
	Parallelogram b and c are sides b = base h = height	Area = bh Perimeter = 2(b + c)
	Rhombus a = length of each side b = base h = height d1, d2 are the diagonal	Area = bh(Formula 1) Area = ½*d1d*2 (Formula 2 ) Perimeter = 4a
	Triangle a , b and c are sides b = base h = height	Area = ½bh (Formula 1) Area(Formula 2) = √S(S−a)(S−b)(S−c where S is the semiperimeter S =(a+b+c)/2 (Formula 2 for area -Heron’s formula) Perimeter = a + b + c Radius of incircle of a triangle of area A =AS where S is the semiperimeter =(a+b+c)/2
	Equilateral Triangle a = side	Area = (√3/4)aa Perimeter = 3a Radius of incircle of an equilateral triangle of side a = a/2*√3 Radius of circumcircle of an equilateral triangle of side a = a/√3
Base a is parallel to base b	Trapezium(Trapezoid in American English) h = height	Area = 12(a+b)h
	Circle r = radius d = diameter	d = 2r Area = πr2 = 14πd2 Circumference = 2πr = πd
	Sector of Circle r = radius θ = central angle	Area = (θ/360) πrr* Arc Length, s = (θ/180) πr In the radian system for angular measurement, 2π radians = 360° => 1 radian = 180°π => 1° = π180 radians Hence, Angle in Degrees = Angle in Radians × 180°π Angle in Radians = Angle in Degrees × π180°
	Ellipse Major axis length = 2a Minor axis length = 2b	Area = πab Perimeter ≈
	Rectangular Solid l = length w = width h = height	Total Surface Area = 2lw + 2wh + 2hl = 2(lw + wh + hl) Volume = lwh
	Cube s = edge	Total Surface Area = 6s² Volume = s³
	Right Circular Cylinder h = height r = radius of base	Lateral Surface Area = (2 π r)h Total Surface Area = (2 π r)h + 2 (π r²) Volume = (π r²)h
	Pyramid h = height B = area of the base	Total Surface Area = B + Sum of the areas of the triangular sides Volume = 1/3Bh
	Right Circular Cone h = height r = radius of base	Lateral Surface Area=πrs where s is the slant height =√rr+hh Total Surface Area =πrs+πr2
	Sphere r = radius d = diameter	d = 2r Surface Area =4πrr=πdd Volume =4/3πrrr=16πddd

Important properties of Geometric Shapes
1. Properties of Triangle
  1. Sum of the angles of a triangle = 180°
  2. Sum of any two sides of a triangle is greater than the third side.

The line joining the midpoint of a side of a triangle to the positive vertex is called the Median

The median of a triangle divides the triangle into two triangles with equal areas
Centroid is the point where the three medians of a triangle meet.
Centroid divides each median into segments with a 2:1 ratio

Area of a triangle formed by joining the midpoints of the sides of a given triangle is one-fourth of the area of the given triangle.
An equilateral triangle is a triangle in which all three sides are equal

In an equilateral triangle, all three internal angles are congruent to each other
In an equilateral triangle, all three internal angles are each 60°
An isosceles triangle is a triangle with (at least) two equal sides

In isosceles triangle, altitude from vertex bisects the base.

Properties of Quadrilaterals
Rectangle
1. The diagonals of a rectangle are equal and bisect each other
2. opposite sides of a rectangle are parallel

opposite sides of a rectangle are congruent

opposite angles of a rectangle are congruent
All four angles of a rectangle are right angles
The diagonals of a rectangle are congruent
Square

All four sides of a square are congruent
Opposite sides of a square are parallel

The diagonals of a square are equal
The diagonals of a square bisect each other at right angles
All angles of a square are 90 degrees.

A square is a special kind of rectangle where all the sides have equal length

Parallelogram

The opposite sides of a parallelogram are equal in length.
The opposite angles of a parallelogram are congruent (equal measure).

The diagonals of a parallelogram bisect each other.

Each diagonal of a parallelogram divides it into two triangles of the same area

Rhombus

All the sides of a rhombus are congruent
Opposite sides of a rhombus are parallel.
The diagonals of a rhombus bisect each other at right angles

Opposite internal angles of a rhombus are congruent (equal in size)

Any two consecutive internal angles of a rhombus are supplementary; i.e. the sum of their angles = 180° (equal in size)
If each angle of a rhombus is 90°, it is a square

Other properties of quadrilaterals

The sum of the interior angles of a quadrilateral is 360 degrees
If a square and a rhombus lie on the same base, area of the square will be greater than area of the rhombus (In the special case when each angle of the rhombus is 90°, rhombus is also a square and therefore areas will be equal)
A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
Of all the parallelogram of given sides, the parallelogram which is a rectangle has the greatest area.
Each diagonal of a parallelogram divides it into two triangles of the same area
A square is a rhombus and a rectangle.

Sum of Interior Angles of a polygon
1. The sum of the interior angles of a polygon = 180(n – 2) degrees where n = number of sides Example 1 : Number of sides of a triangle = 3. Hence, sum of the interior angles of a triangle = 180(3 – 2) = 180 × 1 = 180 ° Example 2 : Number of sides of a quadrilateral = 4. Hence, sum of the interior angles of any quadrilateral = 180(4 – 2) = 180 × 2 = 360.

Solved Examples

Level 1

An error 2% in excess is made while measuring the side of a square. What is the Percentage of error in the calculated area of the square?
4.04 %
2.02 %
4 %
2 %

Answer : Option A

Explanation :

Error = 2% while measuring the side of a square.

Let the correct value of the side of the square = 100
Then the measured value = (100×(100+2))/100=102 (∵ error 2% in excess)

Correct Value of the area of the square = 100 × 100 = 10000
Calculated Value of the area of the square = 102 × 102 = 10404

Error = 10404 – 10000 = 404
Percentage Error = (Error/Actual Value)×100=(404/10000)×100=4.04%

A towel, when bleached, lost 20% of its length and 10% of its breadth. What is the percentage of decrease in area?
30 %
28 %
32 %
26 %

Answer : Option B

Explanation :
Let original length = 100 and original breadth = 100
Then original area = 100 × 100 = 10000

Lost 20% of length
=> New length =( Original length × (100−20))/100
=(100×80)/100=80

Lost 10% of breadth
=> New breadth= (Original breadth × (100−10))/100
=(100×90)/100=90

New area = 80 × 90 = 7200

Decrease in area
= Original Area – New Area
= 10000 – 7200 = 2800

Percentage of decrease in area
=(Decrease in Area/Original Area)×100=(2800/10000)×100=28%

If the length of a rectangle is halved and its breadth is tripled, what is the percentage change in its area?
25 % Increase
25 % Decrease
50 % Decrease
50 % Increase

Answer : Option D

Explanation :
Let original length = 100 and original breadth = 100
Then original area = 100 × 100 = 10000

Length of the rectangle is halved
=> New length = (Original length)/2=100/2=50

breadth is tripled
=> New breadth= Original breadth × 3 = 100 × 3 = 300

New area = 50 × 300 = 15000

Increase in area = New Area – Original Area = 15000 – 10000= 5000
Percentage of Increase in area =( Increase in Area/OriginalArea)×100=(5000/10000)×100=50%

The area of a rectangle plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot?
14 metres
20 metres
18 metres
12 metres

Answer : Option B

Explanation:

lb = 460 m² ——(Equation 1)

Let the breadth = b
Then length, l =( b×(100+15))/100=115b/100——(Equation 2)

From Equation 1 and Equation 2,
115b/100×b=460b2=46000/115=400⇒b=√400=20 m

If a square and a rhombus stand on the same base, then what is the ratio of the areas of the square and the rhombus?
equal to ½
equal to ¾
greater than 1
equal to 1

Answer : Option C

Explanation :

If a square and a rhombus lie on the same base, area of the square will be greater than area of the rhombus (In the special case when each angle of the rhombus is 90°, rhombus is also a square and therefore areas will be equal)

Hence greater than 1 is the more suitable choice from the given list

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Note : Proof

Consider a square and rhombus standing on the same base ‘a’. All the sides of a square are of equal length. Similarly all the sides of a rhombus are also of equal length. Since both the square and rhombus stands on the same base ‘a’,

Length of each side of the square = a
Length of each side of the rhombus = a

Area of the sqaure = a² …(1)

From the diagram, sin θ = h/a
=> h = a sin θ

Area of the rhombus = ah = a × a sin θ = a² sin θ …(2)

From (1) and (2)

Area of the square/Area of the rhombus= a² /a²sinθ=1/sinθ

Since 0° < θ < 90°, 0 < sin θ < 1. Therefore, area of the square is greater than that of rhombus, provided both stands on same base.

(Note that, when each angle of the rhombus is 90°, rhombus is also a square (can be considered as special case) and in that case, areas will be equal.

The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 800 m, find out the area of the field.
37500 m²
30500 m²
32500 m²
40000 m²

Answer : Option A

Explanation :

Given that breadth of a rectangular field is 60% of its length
⇒b=(60/100)* l =(3/5)* l

perimeter of the field = 800 m
=> 2 (l + b) = 800
⇒2(l+(3/5)* l)=800⇒l+(3/5)* l =400⇒(8/5)* l =400⇒l/5=50⇒l=5×50=250 m

b = (3/5)* l =(3×250)/5=3×50=150 m

Area = lb = 250×150=37500 m2

What is the percentage increase in the area of a rectangle, if each of its sides is increased by 20%?
45%
44%
40%
42%

Answer : Option B

Explanation :
Let original length = 100 and original breadth = 100
Then original area = 100 × 100 = 10000

Increase in 20% of length.
=> New length = (Original length ×(100+20))/100=(100×120)/100=120

Increase in 20% of breadth
=> New breadth= (Original breadth × (100+20))/100=(100×120)/100=120

New area = 120 × 120 = 14400

Increase in area = New Area – Original Area = 14400 – 10000 = 4400
Percentage increase in area =( Increase in Area /OriginalArea)×100=(4400/10000)×100=44%

What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
814
802
836
900

Answer : Option A

Explanation :

l = 15 m 17 cm = 1517 cm
b = 9 m 2 cm = 902 cm
Area = 1517 × 902 cm²

Now we need to find out HCF(Highest Common Factor) of 1517 and 902.
Let’s find out the HCF using long division method for quicker results

902) 1517 (1

-902

—————–

615) 902 (1

————–

287) 615 (2

-574

—————–

41) 287 (7

-287

————

0
————

Hence, HCF of 1517 and 902 = 41

Hence, side length of largest square tile we can take = 41 cm
Area of each square tile = 41 × 41 cm²

Number of tiles required = (1517×902)/(41×41)=37×22=407×2=814

Level 2

A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, find out the area of the parking space in square feet?
126 sq. ft.
64 sq. ft.
100 sq. ft.
102 sq. ft.

Answer : Option A

Explanation :

Let l = 9 ft.

Then l + 2b = 37
=> 2b = 37 – l = 37 – 9 = 28
=> b = 282 = 14 ft.

Area = lb = 9 × 14 = 126 sq. ft.

A large field of 700 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the Average of the two areas. What is the area of the smaller part in hectares?
400
365
385
315

Answer : Option D

Explanation :

Let the areas of the parts be x hectares and (700 – x) hectares.

Difference of the areas of the two parts = x – (700 – x) = 2x – 700

one-fifth of the average of the two areas = 15[x+(700−x)]2
=15×7002=3505=70

Given that difference of the areas of the two parts = one-fifth of the average of the two areas
=> 2x – 700 = 70
=> 2x = 770
⇒x=7702=385

Hence, area of smaller part = (700 – x) = (700 – 385) = 315 hectares.

The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle?
18 cm
16 cm
40 cm
20 cm

Answer : Option C

Explanation :

Let breadth = x cm
Then length = 2x cm
Area = lb = x × 2x = 2x²

New length = (2x – 5)
New breadth = (x + 5)
New Area = lb = (2x – 5)(x + 5)

But given that new area = initial area + 75 sq.cm.
=> (2x – 5)(x + 5) = 2x² + 75
=> 2x² + 10x – 5x – 25 = 2x² + 75
=> 5x – 25 = 75
=> 5x = 75 + 25 = 100
=> x = 1005 = 20 cm

Length = 2x = 2 × 20 = 40cm

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then what is the area of the park (in sq. m)?
142000
112800
142500
153600

Answer : Option D

Explanation :

l : b = 3 : 2 —-(Equation 1)

Perimeter of the rectangular park
= Distance travelled by the man at the speed of 12 km/hr in 8 minutes
= speed × time = 12×860 (∵ 8 minute = 860 hour)
= 85 km = 85 × 1000 m = 1600 m

Perimeter = 2(l + b)

=> 2(l + b) = 1600
=> l + b = 16002 = 800 m —-(Equation 2)

From (Equation 1) and (Equation 2)
l = 800 × 35 = 480 m
b = 800 × 25 = 320 m (Or b = 800 – 480 = 320m)

Area = lb = 480 × 320 = 153600 m²

It is decided to construct a 2 metre broad pathway around a rectangular plot on the inside. If the area of the plots is 96 sq.m. and the rate of construction is Rs. 50 per square metre., what will be the total cost of the construction?
Rs.3500
Rs. 4200
Insufficient Data
Rs. 4400

Answer : Option C

Explanation :
Let length and width of the rectangular plot be l and b respectively
Total area of the rectangular plot = 96 sq.m.
=> lb = 96

Width of the pathway = 2 m
Length of the remaining area in the plot = (l – 4)
breadth of the remaining area in the plot = (b – 4)
Area of the remaining area in the plot = (l – 4)(b – 4)

Area of the pathway
= Total area of the rectangular plot – remaining area in the plot
= 96 – [(l – 4)(b – 4)]
= 96 – [lb – 4l – 4b + 16]
= 96 – [96 – 4l – 4b + 16]
= 96 – 96 + 4l + 4b – 16
= 4l + 4b – 16
= 4(l + b) – 16

We do not know the values of l and b and hence area of the pathway cannot be found out. So we cannot determine total cost of the construction.

A circle is inscribed in an equilateral triangle of side 24 cm, touching its sides. What is the area of the remaining portion of the triangle?
144√3−48π cm²
121√3−36π cm²
144√3−36π cm²
121√3−48π cm²

Answer : Option A

Explanation :
Area of an equilateral triangle = (3/√4)*a *a where a is length of one side of the equilateral triangle
Area of the equilateral Δ ABC = (3/√4)*a *a = (3/√4)*24*24=144√3 cm2⋯ (1)

Area of a triangle = 12bhwhere b is the base and h is the height of the triangle
Let r = radius of the inscribed circle. Then
Area of Δ ABC
= Area of Δ OBC + Area of Δ OCA + area of Δ OAB
= (½ × r × BC) + (½ × r × CA) + (½ × r × AB)
= ½ × r × (BC + CA + AB)
= ½ x r x (24 + 24 + 24)
= ½ x r x 72 = 36r cm² —-(2)

From (1) and (2),
144√3=36r⇒r=144√3/36=4√3−−−−(3)

Area of a circle = πr2 where = radius of the circle
From (3), the area of the inscribed circle = πr2=π(4√3)* (4√3)=48π⋯(4)

Hence, area of the remaining portion of the triangle
= Area of Δ ABC – Area of inscribed circle
144√3−48π cm2

What will be the length of the longest rod which can be placed in a box of 80 cm length, 40 cm breadth and 60 cm height?
√11600 cm
√14400 cm
√10000 cm
√12040 cm

Answer : Option A

Explanation :
The longest road which can fit into the box will have one end at A and other end at G (or any other similar diagonal).
Hence the length of the longest rod = AG

Initially let’s find out AC. Consider the right angled triangle ABC

AC² = AB² + BC² = 40² + 80² = 1600 + 6400 = 8000
⇒AC = √8000 cm

Consider the right angled triangle ACG

AG² = AC² + CG²
(√8000)²+60²=8000+3600=11600
=> AG = √11600 cm
=> Length of the longest rod = √11600cm

A rectangular plot measuring 90 metres by 50 metres needs to be enclosed by wire fencing such that poles of the fence will be kept 5 metres apart. How many poles will be needed?
30
44
56
60

Answer : Option C

Explanation :

Perimeter of a rectangle = 2(l + b)
where l is the length and b is the breadth of the rectangle

Length of the wire fencing = perimeter = 2(90 + 50) = 280 metres
Two poles will be kept 5 metres apart. Also remember that the poles will be placed along the perimeter of the rectangular plot, not in a single straight line which is very important.
Hence number of poles required = 280/5 = 56,

Mensuration is the process of measuring the dimensions of objects. It is a branch of mathematics that deals with the measurement of length, area, volume, and other properties of objects.

Area is the amount of space enclosed by a two-dimensional figure. It is measured in square units, such as square inches, square centimeters, or square meters. The area of a rectangle is equal to its length times its width. The area of a circle is equal to pi times the square of its radius.

Circumference is the distance around a closed curve. It is measured in linear units, such as inches, centimeters, or meters. The circumference of a circle is equal to two times pi times its radius.

Volume is the amount of space enclosed by a three-dimensional figure. It is measured in cubic units, such as cubic inches, cubic centimeters, or cubic meters. The volume of a rectangular prism is equal to its length times its width times its height. The volume of a sphere is equal to four-thirds pi times the cube of its radius.

Density is the mass of an object per unit volume. It is measured in grams per cubic centimeter or kilograms per cubic meter. The density of an object can be calculated by dividing its mass by its volume.

Weight is the force of gravity on an object. It is measured in pounds or kilograms. The weight of an object can be calculated by multiplying its mass by the acceleration due to gravity.

Mass is the amount of matter in an object. It is measured in grams or kilograms. The mass of an object does not change, regardless of its location.

Length is the Distance Between Two Points. It is measured in linear units, such as inches, centimeters, or meters. The length of a line segment is equal to the distance between its endpoints.

Width is the distance from one side of an object to the other. It is measured in linear units, such as inches, centimeters, or meters. The width of a rectangle is equal to the distance between its two parallel sides.

Height is the distance from the bottom to the top of an object. It is measured in linear units, such as inches, centimeters, or meters. The height of a rectangle is equal to the distance between its two non-parallel sides.

Angle is the measure of the amount of turn between two lines or rays. It is measured in degrees or radians. A right angle is an angle that measures 90 degrees. A straight angle is an angle that measures 180 degrees.

Radius is the distance from the center of a circle to any point on its circumference. It is measured in linear units, such as inches, centimeters, or meters.

Diameter is the distance across a circle through its center. It is equal to twice the radius.

Pi is a mathematical constant that is approximately equal to 3.14. It is the ratio of the circumference of a circle to its diameter.

Square is a four-sided figure with all sides of equal length and all angles of equal measure (90 degrees).

Cube is a three-dimensional figure with six square faces.

Prism is a three-dimensional figure with two parallel bases that are polygons and lateral faces that are rectangles.

Cylinder is a three-dimensional figure with two parallel circular bases and a curved lateral surface.

Cone is a three-dimensional figure with a circular base and a curved lateral surface that meets the base at a single point.

Sphere is a three-dimensional figure with all points on its surface equidistant from its center.

Pyramid is a three-dimensional figure with a polygonal base and four or more triangular faces that meet at a single point.

Parallelogram is a four-sided figure with opposite sides parallel and opposite angles congruent.

Trapezoid is a four-sided figure with one pair of parallel sides.

Rectangle is a four-sided figure with opposite sides parallel and opposite angles congruent, and all angles of equal measure (90 degrees).

Rhombus is a four-sided figure with all sides of equal length, but opposite angles are not congruent.

Triangle is a three-sided figure with three angles that add up to 180 degrees.

Pentagon is a five-sided figure.

Hexagon is a six-sided figure.

Heptagon is a seven-sided figure.

Octagon is an eight-sided figure.

Nonagon is a nine-sided figure.

Decagon is a ten-sided figure.

Dodecagon is a twelve-sided figure.

What is the difference between a rectangle and a square?

A rectangle is a four-sided shape with four right angles. A square is a rectangle with all four sides of equal length.

What is the difference between a circle and an oval?

A circle is a round shape with all points the same distance from the center. An oval is a shape that is similar to a circle but is not perfectly round.

What is the difference between a triangle and a trapezoid?

A triangle is a three-sided shape with three angles that add up to 180 degrees. A trapezoid is a four-sided shape with one pair of parallel sides.

What is the difference between a parallelogram and a rhombus?

A parallelogram is a four-sided shape with opposite sides parallel and opposite angles congruent. A rhombus is a parallelogram with all four sides of equal length.

What is the difference between a kite and a kite?

A kite is a four-sided shape with two pairs of adjacent sides of equal length and opposite angles congruent. A kite is a type of kite that is flown in the air.

What is the difference between a regular polygon and an irregular polygon?

A regular polygon is a polygon with all sides of equal length and all angles of equal measure. An irregular polygon is a polygon with sides of unequal length and angles of unequal measure.

What is the difference between a convex polygon and a concave polygon?

A convex polygon is a polygon in which all interior angles are less than 180 degrees. A concave polygon is a polygon in which at least one interior angle is greater than 180 degrees.

What is the difference between a right angle, an acute angle, and an obtuse angle?

A right angle is an angle that measures 90 degrees. An acute angle is an angle that measures less than 90 degrees. An obtuse angle is an angle that measures more than 90 degrees.

What is the difference between a line segment and a ray?

A line segment is a part of a line with two endpoints. A ray is a part of a line with one endpoint and extends infinitely in the other direction.

What is the difference between a point, a line, and a plane?

A point is a location in space. A line is a one-dimensional figure that extends infinitely in both directions. A plane is a two-dimensional figure that extends infinitely in all directions.

What is the difference between a solid, a surface, and a volume?

A solid is a three-dimensional figure. A surface is a two-dimensional figure that forms the boundary of a solid. A volume is the amount of space enclosed by a solid.

What is the difference between a sphere, a cube, and a cylinder?

A sphere is a three-dimensional figure with all points the same distance from the center. A cube is a three-dimensional figure with six square faces. A cylinder is a three-dimensional figure with two circular bases and a curved surface.

What is the difference between a cone, a pyramid, and a prism?

A cone is a three-dimensional figure with a circular base and a curved surface that meets at a point called the vertex. A pyramid is a three-dimensional figure with a polygonal base and four or more triangular faces that meet at a point called the vertex. A prism is a three-dimensional figure with two parallel bases and rectangular or square faces.

What is the difference between a surface area and a volume?

The surface area of a solid is the total area of all of its faces. The volume of a solid is the amount of space enclosed by its surface.

Sure, here are some MCQs without mentioning the topic MENSURATION:

What is the area of a rectangle with a length of 10 cm and a width of 5 cm?
(A) 25 cm2
(B) 50 cm2
(C) 100 cm2
(D) 200 cm2
What is the volume of a cube with a side length of 5 cm?
(A) 125 cm3
(B) 500 cm3
(C) 1250 cm3
(D) 625 cm3
What is the circumference of a circle with a radius of 5 cm?
(A) 10 cm
(B) 25 cm
(C) 50 cm
(D) 78.5 cm
What is the area of a circle with a radius of 5 cm?
(A) 78.5 cm2
(B) 25 cm2
(C) 100 cm2
(D) 500 cm2
What is the volume of a sphere with a radius of 5 cm?
(A) 523.598775 cm3
(B) 500 cm3
(C) 125 cm3
(D) 625 cm3
What is the surface area of a sphere with a radius of 5 cm?
(A) 490.39 cm2
(B) 500 cm2
(C) 125 cm2
(D) 625 cm2
What is the slant height of a cone with a radius of 5 cm and a height of 10 cm?
(A) 12.7 cm
(B) 17.32 cm
(C) 25 cm
(D) 50 cm
What is the volume of a cone with a radius of 5 cm and a height of 10 cm?
(A) 125 cm3
(B) 250 cm3
(C) 500 cm3
(D) 1250 cm3
What is the surface area of a cone with a radius of 5 cm and a height of 10 cm?
(A) 125 cm2
(B) 250 cm2
(C) 500 cm2
(D) 1250 cm2
What is the area of a trapezoid with bases of 10 cm and 15 cm and a height of 5 cm?
(A) 50 cm2
(B) 75 cm2
(C) 100 cm2
(D) 150 cm2
What is the volume of a pyramid with a base area of 10 cm2 and a height of 5 cm?
(A) 25 cm3
(B) 50 cm3
(C) 100 cm3
(D) 125 cm3
What is the surface area of a pyramid with a base area of 10 cm2 and a height of 5 cm?
(A) 50 cm2
(B) 75 cm2
(C) 100 cm2
(D) 150 cm2
What is the area of a right triangle with a hypotenuse of 10 cm and a leg of 5 cm?
(A) 25 cm2
(B) 50 cm2
(C) 100 cm2
(D) 125 cm2
What is the volume of a right circular cylinder with a radius of 5 cm and a height of 10 cm?
(A) 125 cm3
(B) 250 cm3
(C) 500 cm3
(D) 1250 cm3
What is the surface area of a right circular cylinder with a radius of 5 cm and a height of 10 cm?
(A) 125 cm2
(B) 250 cm2
(C) 500 cm2
(D) 1250 cm2