Question

# The formula for the volume of a cylinder is V = πr²h.

Solid Geometry

The formula for the volume of a cylinder is $$V = \pi r^{2}h$$. What is the radius for a cylinder that has a volume of $$160 \pi m^{3}$$ and a height of 8 m? Express your answer in simplest radical form and as a decimal rounded to the nearest tenth.

2021-01-01

Using the given formula, we solve for r: $$\displaystyle{V}=\pi r^{2}h$$
Divide both sides by $$\pi h$$

$$V/ \pi h=r^{2}$$

Take the square root:

$$r=\sqrt{V/πh}$$

Substitute $$V=160\pi m^{3}$$ and $$h=8m$$

$$r=\sqrt{160\pi/\pi(8)}$$

$$r=\sqrt{20}$$

$$r=\sqrt{4 \cdot 5}$$

$$r=2\sqrt{m} ~ 4.5 m$$