Question

Find the volume of the follwing figure.

• A. $28\pi {\text{cm}}^3$
• B. $24\pi {\text{cm}}^3$
• C. $36\pi {\text{cm}}^3$
• D. $12\pi {\text{cm}}^3$

Answer 1

The correct option is A $28\pi {\text{cm}}^3$

Observe the given figure, the radius of cone is $r=2\text{cm}$ and its height is $h=3\text{cm}$.

Substitute the value of radius and height of cone in the formula of volume of cone, to calculate its value.

$\begin{array}{cc}\text{Volume of cone}& =\frac{1}{3}\pi r^{2}h\\ & =\frac{1}{3}\pi \left(2{)}^2\right(3)\\ & =4\pi c{m}^3\end{array}$

Now, the radius of cylinder is given as $2\text{cm}$ and its height as $6\text{cm}$, therefore its volume is calculated as,

$\begin{array}{cc}\text{Volume of cylinder}& =\pi r^{2}h\\ & =\pi \left(2{)}^2\right(6)\\ & =4\left(6\right)\pi \\ & =24\pi c{m}^3\end{array}$

Thus, the volume of the given figure is commuted as,

$\begin{array}{cc}\text{Volume of given figure}& =\text{Volume of cone}+\text{Volume of cylinder}\\ & =4\pi c{m}^3+24\pi c{m}^3\\ & =28\pi c{m}^3\end{array}$

Hence, the required volume is $28\pi {\text{cm}}^3$.