Question

A cylinder has a volume of 224 ft3 and a height of 14 ft. What is the diameter of the cylinder?

Option 1: 4 ft
Option 2: 6 ft
Option 3: 8 ft
Option 4: 10 ft

Answer 1

The diameter of a cylinder with a volume of 224 ft³ and a height of 14 ft is 8 ft.

Step-by-step explanation:

To find the diameter of a cylinder when given its volume and height, we use the formula for the volume of a cylinder: V = πr²h, where V is the volume, r is the radius, and h is the height of the cylinder. In this case, we have the volume V as 224 ft³ and the height h as 14 ft.

First, we rearrange the formula to solve for the radius r:
r = sqrt(V / (πh)). Plugging in the volume and height gives us:

r = sqrt(224 ft³ / (π * 14 ft))

= sqrt(224 / (3.14159 * 14))

= sqrt(16)

So, the radius r is 4 ft. Since the diameter is twice the radius, the diameter d is 8 ft. Therefore, the correct answer is Option 3: 8 ft.