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Answer :
Final answer:
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.
Learn more about Radius calculation here:
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