# Ex.13.6 Q4 Surface Areas and Volumes Solution - NCERT Maths Class 9

## Question

If the lateral surface of a cylinder is \(92.4\,\,\rm cm^2 \) and its height is \(5\; \rm cm\), then find

(i) radius of its base.

(ii) its volume. (Use \(\pi = 3.14\))

## Text Solution

**Reasoning:**

Lateral surface area of a cylinder is \(2\pi rh \).

Volume of cylinder is \( \pi {r^2}h.\)

**What is known?**

Lateral surface area of the cylinder and its height.

**What is unknown?**

Base radius.

**Steps:**

Lateral surface area of a cylinder having \(r\) as radius and height \(h\) is \( 2\pi rh \)

Lateral surface area \( = 94.2\, \rm cm^2 \)

\(\text{Height}\; h = 5\; \rm cm\)

\(\begin{align}2\pi rh &= 94.2\\2 \times 3.14 \times r \times 5 &= 94.2\\r &= \frac{{94.2}}{{5 \times 3.14 \times 2}} \\ & = 3\,\,\rm cm \end{align}\)

**What is unknown?**

Volume of the cylinder.

**Steps:**

\(\text{Radius}\; r = 3\; \rm cm\)

\(\text{Height}\; h = 5\; \rm cm\)

Volume of cylinder

\[\begin{align} & =\pi r^{2} h \\ & =3.14 \times 3 \times 3 \times 5 \\ & =141.3 \, \mathrm{cm}^{3}\end{align} \]

**Answer:**

\(\text{Radius of its base} = 3\; \rm cm\)

Its volume \( = 141.3\,\, \rm cm^3 \)