High School

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 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

Answer :

Final answer:

Applying the formula for the volume of a cone and solving for the radius, we find that the radius of the conical water reservoir is approximately 5.03 feet, which corresponds to the option 'c'.

Explanation:

To find the radius of the conical water reservoir, we first need to understand the formula for the volume of a cone, which is given as V = 1/3πr²h, where V represents the volume, r the radius, and h the height.

In this case, we know that V = 225 cubic feet and h = 8.5 feet. Therefore, we can rearrange the formula to solve for r, getting r = √(3V/πh). Substituting the given values, we get r = √(3*225/π*8.5) ≈ 5.03 feet.

Thus, based on the specifications given and the volume of a cone formula, the radius of the water reservoir is approximately 5.03 feet, making option 'c' the correct choice.

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