# Ex.13.3 Q2 Surface Areas and Volumes Solution - NCERT Maths Class 9

## Question

Find the total surface area of a cone, if its slant height is \(21\,\rm m\) and diameter of its base is \(24 \,\rm m.\)

## Text Solution

**Reasoning:**

The total surface area of the cone is the sum of the curved surface area and area of the base which is a circle.

**What is known?**

Diameter of the box and slant height of the cone.

**What is unknown?**

Total surface area of the cone.

**Steps:**

Total surface area of the cone is

\(= \pi rl + \pi {r^2} = \pi r(l + r) \)

Where \(l\) is slant height and radius \(r.\)

Diameter \(= 2r = 24 \rm\,m\)

\(r = 12{\rm m}\\ \\ l = 21 \rm m\)

**T S A **\(= \pi r(l + r) \)

\(\begin{align} &= \frac{{22}}{7} \times 12 \times (12 + 21)\\ &= \frac{{22}}{7} \times 12 \times 33 \\ &= \frac{{8712}}{7} = 1244.57\,\,{\rm{m}}^2 \end{align}\)

**Answer:**

Total surface area of the cone \(\begin{align} = 1244.57\,{\rm{m}}^2 \end{align}\)