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

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## Question

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

Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-3 | Question 2

## 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}

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