Question

Designing a Container You are designing a container in the shape of a cylinder. The radius is 12 inches. You want the container to hold at most 6048 pi cubic inches. What is the greatest possible height of the container? ​

Answer 1

To find the greatest possible height of the container, we need to solve the volume formula of a cylinder for the height.

Step-by-step explanation:

To find the greatest possible height of the container, we need to solve the volume formula of a cylinder for the height. The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height. Since we want the container to hold at most 6048π cubic inches, we can set up the equation:

6048π = (π(12)²)h

Now, we can simplify the equation to find the value of h:

6048π = 144πh

Dividing both sides of the equation by 144π gives us:

h = 6048/144