Question

A right angled $△ABC$ with sides $5cm,12cm$ and $13cm$ is revolved about the fixed side of $12cm$. Find the volume of the solid generated.

• A. $314\frac{2}{7}{cm}^3$
• B. $314\frac{1}{7}{cm}^3$
• C. $34\frac{2}{7}{cm}^3$
• D. None of these

Answer 1

The correct option is A $314\frac{2}{7}{cm}^3$

Consider the given right triangle $ABC$ with sides $5cm,12cm$ and $13cm$.

When it is revolved about the fixed side of $12cm$, then it will generate a solid cone with height $12cm$ and radius $5cm$.

We know that the volume of the cone

$V=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\times \frac{22}{7}\times 5^2\times 12$

$=\frac{22}{7}\times 25\times 4$

$=\frac{22}{7}\times 100$

$=\frac{2200}{7}$

$=314\frac{2}{7}c{m}^3$.

Hence, option $A$ is correct.