Question

find the volume of the figure below. as you can see the question has already been answered but my teacher wants me to show how she got the answer.

Answer 1

Step 1: List the figures in the composite image:

The composite image consists of a cylinder and a hemisphere.

Therefore, the volume V is given by

$V\text{ =}\pi r^2(\frac{2}{3}r+h)$

where

$\begin{gathered} \text{radius}=\frac{diameter}{2}=\frac{18}{2}=9\text{ inch} \\ \text{height = (30-9) inches} \\ \text{height =21 inches} \end{gathered}$

Therefore, the volume is

$\begin{gathered} V=\pi(9)^2(\frac{2}{3}\times9+21) \\ V=\pi\times81(6+21) \\ V=\pi(2187) \\ So\text{ the volume = 2187}\pi\text{ in}^3 \end{gathered}$

Option D is correct