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# A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in between.

**Solution:**

Given, side of cube = 4 cm

A cube contains a sphere touching its sides

We have to find the volume of the gap in between

Volume of gap in between = volume of cube - volume of sphere

Volume of cube = (side)³

= (4)³

= 64 cm³

Since the sphere is inside the cube, the diameter of the sphere = 4 cm

So, radius of the sphere = 2 cm

Volume of sphere = 4/3 πr³

Where, r is the radius of the sphere

= 4/3 (22/7)(2)³

= 4(22)(8)/21

= 32(22)/21

= 704/21

= 33.52 cm³

Volume of gap in between = 64 - 33.52

= 30.48 cm³

Therefore, the volume of the gap in between is 30.48 cm³.

**✦Try This: **A cube of side 5 cm contains a sphere touching its sides. Find the volume of the gap in between.

**☛ Also Check:** NCERT Solutions for Class 9 Maths Chapter 13

**NCERT Exemplar Class 9 Maths Exercise 13.4 Problem 6**

## A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in between.

**Summary:**

A cube of side 4 cm contains a sphere touching its sides. The volume of the gap in between is 30.48 cm³

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