# Ex.13.3 Q3 Surface Areas and Volumes Solution - NCERT Maths Class 9

Go back to  'Ex.13.3'

## Question

Curved surface area of a cone is \begin{align}308\,\,c{m^2} \end{align} and its slant height is $$14\rm\, cm.$$ Find

(ii) Total surface area of the cone.

## Text Solution

Reasoning:

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

What is known?

Curved surface area of the cone and its slant height.

What is unknown?

Steps:

Curved surface area $$=$$ \begin{align}\,\,\pi rl = 308\,\,{\rm{cm}}^2 \end{align}

Slant height ($$l$$) $$= 14\,\rm cm$$

\begin{align}\pi rl &= 308 \\\frac{{22}}{7} \times r \times 14 &= 308 \\r &= \frac{{308}}{{14}} \times \frac{7}{{22}} = 7\,\,\rm cm\end{align}

(ii) Total surface area of the cone.

Steps:

Total surface area \begin{align}\, = \pi r\,(l + r) \end{align}

Radius $$= 7 \rm\,cm$$

Slant height ($$l$$) $$= 14\,\rm cm$$

\begin{align}\rm TSA &= \pi r(r + l) \\ &= \frac{{22}}{7} \times 7 \times (7 + 14) \\ &= 22 \times 21 \\ & = 462\,\,\rm c{m^2} \end{align}

Radius of the cone $$= 7\,\rm cm$$
Total surface area of the cone $$= 462\, \rm cm^2$$