Question

A cylinder has a radius twice its height and a volume of 32π
`ft^(3)`

What is the cylinder’s radius?

Answer 1

To determine the cylinder's radius, we use the volume formula V = πr²h. With the volume given as 32π and the radius being twice the height, we find that the height is 2 feet, thus the radius is 4 feet.

Step-by-step explanation:

To find the cylinder's radius given that its volume is 32π cubic feet and the radius is twice the height, we need to use the formula V = πr²h. Let's denote the height as h. This means that the radius r = 2h. Plugging this into the volume formula gives us:

V = π(2h)²h = π(4h²)h = 4πh³

Since we know the volume V is 32π, we can set the formulas equal to find the height:

32π = 4πh³

Dividing both sides by 4π, we get:

8 = h³

Therefore, the height h is the cube root of 8, which is 2 feet. Remember, the radius is twice the height, so the radius is 4 feet.