# Find the volume?

## My teacher requires work being shown, if it is not to much of a hassle. Please show work!!! Thank you!!!!

Mar 3, 2017

Volume is $7749.26$ $c {m}^{3}$

#### Explanation:

Although the figure is faded, it appears to be a cylinder whose radius is $10$ $c m s .$ and height is $18$ $c m s .$ and is topped by a hemisphere of the same radius i.e. $10$ $c m s .$

Formula for the volume of cylinder is $\pi \times {r}^{2} \times h$, where $r$ is radius and $h$ is its height. Hence the volume is

$\pi \times {10}^{2} \times 18 = 1800 \pi$

Formula for the volume of sphere is $\frac{4}{3} \times \pi \times {r}^{3}$, but as we have a hemisphere, it should be $\frac{2}{3} \times \pi \times {r}^{3}$ and volume of hemisphere is

$\frac{2}{3} \times \pi \times {10}^{3} = \frac{2000}{3} \times \pi$

and volume of shown object is sum of these i.e.

$\left(1800 + \frac{2000}{3}\right) \times \pi = \frac{7400}{3} \times 3.1416 = 7749.26$ $c {m}^{3}$

Note : AS the figure is faded, in case dimensions are different, you can use above method to calculate the volume of the object.