# If the lateral surface of a cylinder is 92.4 cm^{2} and its height is 5 cm, then find

(i) radius of its base (ii) its volume. (Use π = 3.14)

**Solution:**

Since the lateral surface area and height are known, we can easily obtain the radius and its volume.

Lateral surface area (CSA) of a cylinder of base radius r, and height h = 2πrh

The volume of a cylinder of base radius r, and height h = πr^{2} h

(i) Let the radius of the cylinder be r.

Height of the cylinder, h = 5 cm

Lateral surface area = 92.4 cm^{2}

2πrh = 92.4

r = 92.4 / 2hπ

r = 92.4 / (2 × 5 × 3.14)

r = 3 cm (approx.)

(ii) Volume of cylinder = πr^{2}h

= 3.14 × 3 cm × 3 cm × 5 cm

= 141.3 cm^{3}

Thus, the radius of the base is 3 cm and the volume is 141.3 cm^{3}.

**Video Solution:**

## If the lateral surface of a cylinder is 92.4 cm² and its height is 5 cm, then find i) radius of its base ii) its volume. (Use π = 3.14)

### NCERT Solutions for Class 9 Maths - Chapter 13 Exercise 13.6 Question 4:

**Summary:**

It is given that the lateral surface of a cylinder is 92.4 cm^{2} and its height is 5 cm. We have found that the radius of the base is 3cm and the volume is 141.3 cm^{3}.