If a cubical container of length, breadth and height each of 10 cm can contain exactly 1 litre of water, then a spherical container of radius 10.5 cm can contain
not more than 4 litres of water
more than 4 litres but less than 4.5 litres of water
more than 4.5 litres but less than 5 litres of water
more than 5 litres of water
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CAPF – 2018
Given that this container holds exactly 1 litre, we know 1 litre = 1000 cm³.
A spherical container has a radius of 10.5 cm.
The volume of a sphere is given by the formula V = (4/3)πr³.
Using π ≈ 22/7:
V = (4/3) * (22/7) * (10.5)³
V = (4/3) * (22/7) * (10.5 * 10.5 * 10.5)
V = (4/3) * (22/7) * (1157.625)
V = (88/21) * 1157.625
V = 4.1904… * 1157.625
V ≈ 4851 cm³
To convert this volume to litres, divide by 1000:
Volume in litres = 4851 cm³ / 1000 cm³/litre = 4.851 litres.
Now compare 4.851 litres with the options:
A) not more than 4 litres (4.851 is more than 4) – Incorrect
B) more than 4 litres but less than 4.5 litres (4.851 is not less than 4.5) – Incorrect
C) more than 4.5 litres but less than 5 litres (4.5 < 4.851 < 5) - Correct D) more than 5 litres (4.851 is not more than 5) - Incorrect