Final answer:
To find the height of a cylindrical rain barrel with a radius of 2 feet and a volume of 30 cubic feet, we use the volume formula for a cylinder. The calculated height is approximately 2.39 feet, and none of the given answer choices are correct.
Step-by-step explanation:
The question is asking to calculate the height of a cylindrical rain barrel given its radius and total volume. To find the height of the cylinder, we use the formula for the volume of a cylinder, V = πr²h, where V is the volume, r is the radius of the base, and h is the height of the cylinder.
We know the radius r = 2 feet and the volume V = 30 cubic feet. Plugging these into the formula, we get:
- 30 = π × (2)² × h
- 30 = π × 4 × h
- 30 = 4πh
- ÷ (4π) ÷ (4π)
- h = 30 / (4π)
Using a calculator, we find h = 30 / (4×3.14) which approximately equals 2.39 feet. Therefore, none of the options given (a. 58 feet, b. 39 feet, c. 57 feet, d. 78 feet) are correct; it seems there might be a typo with the options provided.