Question

what is the volume of this cylinder in cubic inches?
image of a cylinder with radius 5 in. and height 8 in. and four options: 40π, 80π, 200π, 320π

Explanation:

Step1: Recall the formula for the volume of a cylinder.

The formula for the volume \( V \) of a cylinder is \( V = \pi r^2 h \), where \( r \) is the radius of the base and \( h \) is the height of the cylinder.

Step2: Identify the values of \( r \) and \( h \) from the diagram.

From the diagram, the radius \( r = 5 \) inches and the height \( h = 8 \) inches.

Step3: Substitute the values of \( r \) and \( h \) into the formula.

Substitute \( r = 5 \) and \( h = 8 \) into \( V = \pi r^2 h \):
\[

$$\begin{align*} V&=\pi\times(5)^2\times8\\ &=\pi\times25\times8\\ &=\pi\times200\\ & = 200\pi \end{align*}$$

\]

Answer:

\( 200\pi \)