Look at how the given expression $\pi r^2(r+4)$ is built: it is one factor times another factor. Which part matches the base area from the formula you know?

Once you match $\pi r^2$ to the base area, ask: what does the remaining factor have to represent in the cylinder volume formula?

In Desmos, type r = 3 to choose a sample radius. Then type V = pi*r^2*(r + 4) to compute the volume for that radius.

Type H = V/(pi*r^2) to calculate what the height must be using the formula $V = \pi r^2 h$. The value of H is the height for r = 3.

Now enter each option with r = 3: A = pi*r^2*(r + 4), B = pi*r^2, C = r^2, and D = r + 4. Compare each value to H and see which one matches; that matching expression is the correct height formula.

For a cylinder with radius $r$ and height $h$, the volume formula is:

Here, $\pi r^2$ is the area of the circular base, and then we multiply by $h$ (the height).

The problem says the volume can be written as $V = \pi r^2(r+4)$.

Compare this to the formula $V = \pi r^2 h$.

• In both, you see the factor $\pi r^2$.
• In the formula, that factor is multiplied by $h$.
• In the problem, $\pi r^2$ is multiplied by $(r+4)$.

Since $\pi r^2$ represents the base area in both expressions, the other factor must represent the height.

So the height $h$ is represented by $(r+4)$.

Answer: $(r + 4)$.