# If the volume of a right circular cone of height 9 cm is 48π cm^{3}, find the diameter of its base.

**Solution:**

The volume of a cone of base radius 'r', and height 'h', = 1/3πr²h

Volume of the cone = 48π cm³

Height of the cone, 'h' = 9 cm

Radius of the cone, 'r' = ?

1/3πr²h = 48π cm³

r² = 48 cm^{3} × 3 / h

r² = 48 cm^{3} × 3 / 9 cm

r² = 16 cm²

r = √16 cm²

r = 4 cm

Base diameter, 'd' = 2 × radius(r)

= 2 × 4 cm

= 8 cm

The diameter of the box of the right circular cone is 8 cm.

**Video Solution:**

## If the volume of a right circular cone of height 9 cm is 48π cm³, find the diameter of its base.

### NCERT Solutions for Class 9 Maths - Chapter 13 Exercise 13.7 Question 4:

**Summary:**

It is given that the volume of a right circular cone of height 9 cm is 48π cm^{3}. We have found that the diameter of the box of the right circular cone is 8 cm.