# Ex.13.7 Q1 Surface Areas and Volumes Solution - NCERT Maths Class 9

## Question

Assume \begin{align}\pi = \frac{{22}}{7} \end{align} unless stated otherwise

Find the volume of the right circular cone with

(i) radius $$6\rm\, cm,$$ height $$7\rm\, cm$$

(ii) radius $$3.5\rm\, cm,$$ height $$12\rm\, cm$$

Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-7 | Question 1

## Text Solution

Reasoning:

Volume of the cone \begin{align} = \frac{1}{3}\pi {r^2}h \end{align}

Where $$r$$ is base radius and $$h$$ is height.

What is known?

Radius and height of two cones.

What is unknown?

Volume of the cone.

Steps:

Radius $$(r) = 6\rm\, cm$$

Height $$(h) = 7\rm\, cm$$

Volume of cone
\begin{align} & = \frac{1}{3}\pi {r^2}h \\ &= \frac{1}{3} \times \frac{{22}}{7} \times 6 \times 6 \times 7\\ &= \,\,264\,\,\rm c{m^3} \end{align}

Radius $$(r) = 3.5\rm\, cm$$

Height $$(h) = 12\rm\, cm$$

Volume of the cone
\begin{align}&= \frac{1}{3}\pi {r^2}h \\ &= \frac{1}{3} \times \frac{{22}}{7} \times 3.5 \times 3.5 \times 12\\ &= 154\,\,\rm c{m^3} \end{align}

Volume of the cone \begin{align} = 264\,\,\rm c{m^3} \end{align}
Volume of the cone \begin{align} = 154\,\,\rm c{m^3} \end{align}