Question

a cylinder has a volume of 320π cubic inches and a height of 5 inches. what is the radius of the cylinder? a. 4 inches b. 8 inches c. 16 inches d. 32 inches

Explanation:

Step1: Recall volume formula for cylinder

The volume formula of a cylinder is $V=\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height.

Step2: Substitute given values

We know $V = 320\pi$ and $h=5$. Substituting into the formula gives $320\pi=\pi r^{2}\times5$.

Step3: Solve for $r^{2}$

Divide both sides of the equation $320\pi=\pi r^{2}\times5$ by $5\pi$. We get $\frac{320\pi}{5\pi}=r^{2}$, so $r^{2} = 64$.

Step4: Solve for $r$

Take the square - root of both sides. Since $r>0$, $r=\sqrt{64}=8$.

Answer:

B. 8 inches