The ratio of the volume of a cube to that of a sphere which will exactly fit inside the
cube is

(a)  :8 (b)  : 6 (c) 8:  (d) 6: 
the box here refers to pie that is 22/7

Question

The ratio of the volume of a cube to that of a sphere which will
exactly fit inside the
cube is
(a) ï° :8 (b) ï° : 6 (c) 8: ï° (d) 6:
ï°
the box here refers to pie that is 22/7

Lalit Mehra · Accepted Answer

Let the edge of the cube and radius of the sphere be x units and r units.

Since, the sphere exactly fit inside the cube.

∴ Diameter of the sphere = Edge of the cube

$\Rightarrow 2 r = x \frac{Volume of cube}{Volume of sphere} = \frac{x^{3}}{\frac{4}{3} π r^{3}} = \frac{(2 r)^{3}}{\frac{4}{3} π r^{3}} = \frac{8 r^{3}}{\frac{4}{3} π r^{3}} = \frac{6}{π}$

Thus, volume of cube: Volume of sphere = 6 : $π$ .

The ratio of the volume of a cube to that of a sphere which will exactly fit inside thecube is (a)  :8 (b)  : 6 (c) 8:  (d) 6: the box here refers to pie that is 22/7

The ratio of the volume of a cube to that of a sphere which will exactly fit inside the
cube is

(a)  :8 (b)  : 6 (c) 8:  (d) 6: 
the box here refers to pie that is 22/7