A solid metallic sphere of 2 cm radius is melted and converted to a cube. The side of the cube is approximately equal to :
2.4 cm
2.8 cm
3.2 cm
3.6 cm
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CISF-AC-EXE – 2022
Radius of the sphere (r) = 2 cm.
Volume of the sphere (Vsphere) = (4/3)πr³.
Vsphere = (4/3) * π * (2 cm)³ = (4/3) * π * 8 cm³ = (32/3)π cm³.
Let the side of the cube be ‘s’ cm.
Volume of the cube (Vcube) = s³.
Since the volume is conserved, Vcube = Vsphere.
s³ = (32/3)π.
To find ‘s’, we take the cube root: s = ³√[(32/3)π].
Using the approximate value of π ≈ 3.14159:
(32/3)π ≈ (10.6667) * 3.14159 ≈ 33.51 cm³.
s ≈ ³√33.51 cm.
Let’s evaluate the cube of the given options:
A) (2.4)³ ≈ 13.824
B) (2.8)³ ≈ 21.952
C) (3.2)³ ≈ 32.768
D) (3.6)³ ≈ 46.656
The value 3.2³ = 32.768 is closest to 33.51.
– Formula for the volume of a sphere: V = (4/3)πr³.
– Formula for the volume of a cube: V = s³.
– Solve for the side ‘s’ by equating the volumes and taking the cube root.