Question

Find the total volume of the following figure.

• A. $24\pi c{m}^3$
• B. $26\pi c{m}^3$
• C. $30\pi c{m}^3$
• D. $28\pi c{m}^3$

Answer 1

The correct option is D $28\pi c{m}^3$

In the given figure,
radius of the cone, r = 2 cm, and
its height, h = 3 cm

We know,
$\text{Volume of cone}=\frac{1}{3}\pi r^{2}h$

Putting respective values, we get:
$\text{Volume of cone is}$
$=\frac{1}{3}\pi r^{2}h$
$=\frac{1}{3}\pi \left(2{)}^2\right(3)$
$=4\pi c{m}^3$

Now, the radius of cylinder is given as 2cm and its height as 6 cm.

We know,
$\text{Volume of cylinder}=\pi r^{2}h$

Putting respective values, we get:
$\text{Volume of cylinder}$
$=\pi r^{2}h$
$=\pi \left(2{)}^2\right(6)$
$=4\left(6\right)\pi =24\pi c{m}^3$

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

$\text{Volume of given figure}=\text{Volume of cone}$
$+\text{Volume of cylinder}$

$=4\pi c{m}^3+24\pi c{m}^3=28\pi c{m}^3$

Hence, the required volume of the given figure is $28\pi c{m}^3.$