Question

A cube of side 5m contains a sphere touching its sides. Find the volume of the gap in between.

Answer 1

side of the cube is 5 cm
volume = 5 x 5 x 5 = 125cm3
sphere's touches cube sides so diameter of cube is 5 cm 
radius = 5/2 = 2.5 cm
volume of gap in between = 49.10cm3 
is it correct

Answer 2

Answer:

Step-by-step explanation:

Given :-

Each side of the cube (a) = 5 cm  

To Find :-

Volume of gap between cube and sphere.

Formula to be used :-

Volume of the sphere = 4/3πr³

Volume of the cube = a³

Solution :-

Diameter of the sphere (2r) = 5 cm .  

Radius of the sphere (r) = 5/2 cm

Volume of the cube = a³ = 53 cm³ = 125 cm³

Volume of the sphere = 4/3πr³

= 4/3 x 22/7 x (5/2)3  = 4/3 x 22/7 x 5/2 x 5/2 x 5/2

= 65.476 cm3  

Volume of gap between cube and sphere = 125.000 cm³  - 65.476 cm³

Volume of gap between cube and sphere  = 59.524 cm³

Hence, the volume of the gap in between is 60 cm³ (approx)