Ex.13.7 Q7 Surface Areas and Volumes Solution - NCERT Maths Class 9

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Question

A right triangle \(ABC\) with sides \(5\rm\, cm,\) \(12 \rm\,cm\) and \(13\rm\, cm\) is revolved about the side \(12 \rm\,cm.\) Find the volume of the solid so obtained.

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

Text Solution

Reasoning:

Volume of the cone is \(\begin{align}\frac{1}{3} \end{align}\) times of the volume of a cylinder \(\begin{align} = \frac{1}{3}\pi {r^2}h \end{align}\).

What is known?

Sides of the right triangle.

What is unknown?

Volume of the solid obtained.

Steps:

Radius \((r) = 5\rm\, cm\)

height \((h) = 12 \rm\,cm\)

Volume of cone 

\[\begin{align}&= \frac{1}{3}\pi {r^2}h \\ &= \frac{1}{3} \times \frac{{22}}{7} \times 5 \times 5 \times 12\\ &= \frac{{2200}}{7}\,\,or\,\,100\pi \end{align}\]

Answer:

Volume of the cone \(\begin{align}100\pi \,\,\rm\,c{m^3} \end{align}\).