Final answer:
To determine the radius of a cylinder with a known volume of 942 cubic feet and height of 12 feet, the volume formula is rearranged and solved for the radius, resulting in a radius of 6 feet.
Step-by-step explanation:
To find the radius of the cylinder when the volume and height are known, we use the formula for the volume of a cylinder, which is V = πr²h. Here, V is the volume, π is the constant Pi (approximately 3.14), r is the radius, and h is the height of the cylinder. With a given volume of 942 cubic feet and a height of 12 feet, we solve for the radius:
- First, we rearrange the formula to solve for the radius: r² = V / (πh).
- Next, we substitute the values into the formula: r² = 942 / (3.14 × 12).
- Then we calculate the value inside the square root to find r².
- Finally, we take the square root of r² to find r.
After the calculations, the radius of the cylinder is found to be 6 feet, which corresponds to option (b) provided in the question.