# Ex.13.2 Q1 Surface Areas and Volumes - NCERT Maths Class 9

## Question

The curved surface area of a right circular cylinder of height \(14\,\rm{ cm}\) is \(88\,\rm{cm^2}\) . Find the diameter of the base of the cylinder.

## Text Solution

**Reasoning:**

Curved surface area \(\begin{align} = 2\pi rh \end{align}\)

**What is Known?**

Curved surface area of the cylinder and its height.

**What is Unknown?**

Diameter of the base of the cylinder.

**Steps:**

Curved surface area of a cylinder

\(\begin{align} = 2\pi rh = 88\,\rm{cm^2}\,\left( \rm{given} \right) \end{align}\)

Height of the cylinder \(=14\,\rm{ cm}\)

\[\begin{align}2 \times \frac{{22}}{7} \times r \times 14 &= 88\\r = \frac{{88 \times 7}}{{2 \times 22 \times 14}} &= 1\,\rm{cm}\\2 \times \rm{radius} &= \rm{diameter}\\2 \times 1 &= 2\,\rm{cm} \end{align}\]

The diameter of the base of the cylinder \(=\) \(2\, \rm{cm}.\)