Question

You are designing a container in the shape of a cylinder. The radius is 3 inches. You want the container to hold at least 72pie cubic inches. What is the least possible height of the container?

Answer 1

Answer:

8 inches

Step-by-step explanation:

Since we want the volume to be AT LEAST 72π, the volume can be MORE.

So, let's find the least possible height by finding the height it takes for the volume of the cylinder to be 72π.

First, Volume of Cylinder Formula shown below:

Volume of Cylinder = $V_{cyl}=\pi r^2 h$

Now, we will plug in 72π in the volume (V_cyl) and 3 in radius (r=3) and solve for h. Shown below:

$V_{cyl}=\pi r^2 h\\72\pi = \pi (3)^2 h\\72\pi = 9\pi h\\h=\frac{72\pi}{9\pi}\\h=8$

Hence, least possible height is 8 inches