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

## 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

**(i)** Radius of the base

**(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?**

**(i)** Radius of the base.

**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 (\(l\)) \(= 14\,\rm cm\)

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

**Answer:**

Radius of the cone \(= 7\,\rm cm\)

Total surface area of the cone \( = 462\, \rm cm^2 \)