You work for a store that sells built-to-order water reservoirs. Your manager asks you to visit a small business to measure a damaged conical water reservoir for replacement. The label on the water reservoir indicates only the following specifications: The height is 8.5 feet, and, when full, the water reservoir holds 225 cubic feet of water.

Which formula will determine the radius of the water reservoir? Rounded to the nearest hundredth of a foot, what is the radius of the water reservoir?

A. $ r = 0.56 $ feet
B. $ r = 1.69 $ feet
C. $ r = 5.03 $ feet
D. $ r = 8.22 $ feet
E. $ r = 8.71 $ feet

To determine the radius of the conical water reservoir, we use the given volume and height and apply the volume formula for a cone. Thus, solving enables us to conclude that the radius of the water reservoir is approximately 5.03 feet, rounded to the nearest hundredth of a foot.

Explanation:

The given problem requires us to calculate the radius of the water reservoir with known height and volume. The volume V of a conical water reservoir can be calculated using the formula V = (1/3)πr²h, where r is the radius and h is the height.

In this given problem, we have V = 225 cubic feet and h = 8.5 feet. Substituting these values into the formula, we can solve for r. This will provide us with the radius needed to construct the replacement conical water reservoir.

Solving the equation:

A rearrangement of the formula gives r² = (3V)/(πh). Substituting the known quantities we get r² = (3*225)/(π*8.5), which r = √[(3*225)/(π*8.5)].

Using a calculator where possible, it gives the radius of the water reservoir as approximately 5.03 feet.

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