# ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.3 in Chapter 17 - Mensuration

Question 15 Mensuration Exercise 17.3

A cube of side 4 cm contains a sphere touching its sides.

Find the volume of the gap in between.

Solution:

A cube's volume is the total amount of space it takes up in three dimensions. Six square faces make up a cube, a solid object in three dimensions with equal-length sides.

Given side of the cube, a = 4 cm

Volume of the cube = a3

= 43

= 4×4×4

= 64 cm3

Diameter of the sphere = 4 cm

So radius of the sphere, r = d/2 = 4/2 = 2 cm

Volume of the sphere = (4/3)π r3

= (4/3)×(22/7)×23

= 33.523

= 33.52 cm3 (approx)

Volume of the gap in between = 64 – 33.52

= 30.48

= 30.5 cm3 (approx)

Hence the volume of the gap between the cube and sphere is 30.5 cm3.

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