Final answer:
The question involves finding the radius of a bucket with a known volume and height using the formula for the volume of a cylinder. By rearranging the formula to solve for the radius and substituting the provided volume and height, we compute the radius value.
Step-by-step explanation:
The question is asking for the radius of a bucket with a known volume and height, which is a geometry problem in the mathematics subject area. The formula for the volume of a cylinder (which is the shape of the bucket) is V = πr²h, where V is the volume, r is the radius, and h is the height. For the given volume of 765 in.³ and height of 11.2 in., we can rearrange the formula to solve for the radius r:
V = πr²h
765 in.³ = π * r² * 11.2 in.
r² = 765 in.³ / (π * 11.2 in.)
r = √(765 in.³ / (π * 11.2 in.))
After calculating using the value of π (approximately 3.14), we find the radius of the bucket. It's important to use a calculator to ensure accuracy in the calculations.