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

Answer:

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

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

Learn from the best math teachers and top your exams

  • Live one on one classroom and doubt clearing
  • Practice worksheets in and after class for conceptual clarity
  • Personalized curriculum to keep up with school