To find the height of the cylinder, we need to use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius of the base, and h is the height of the cylinder.
Given:
- Area of the base (A) = 452.16 ft²
- Volume (V) = 2,712.96 ft³
First, we need to find the radius of the base (r) using the formula for the area of a circle, A = πr². Since the base of a cylinder is a circle, we can find the radius by:
452.16 = πr²
r² = 452.16/π
r ≈ √(452.16/π)
r ≈ √(144)
r ≈ 12 ft
Now, we can substitute the values of the radius and volume into the volume formula to find the height:
2,712.96 = π(12)²h
2,712.96 = 144πh
h = 2,712.96 / 144π
h ≈ 6 ft
Therefore, the height of the cylinder is approximately 6 feet.
