Find the volume of a right circular cone that has a height of 11.9 ft and a base with a radius of 16.3 ft. Round your answer to the nearest tenth of a cubic foot.
Question
Find the volume of a right circular cone that has a height of 11.9 ft and a base with a radius of 16.3 ft. Round your answer to the nearest tenth of a cubic foot.
Solution
The volume V of a right circular cone can be found using the formula V = 1/3 * π * r² * h, where r is the radius of the base and h is the height of the cone.
Step 1: Substitute the given values into the formula. V = 1/3 * π * (16.3 ft)² * 11.9 ft
Step 2: Square the radius. V = 1/3 * π * 265.69 ft² * 11.9 ft
Step 3: Multiply the squared radius by the height. V = 1/3 * π * 3163.211 ft³
Step 4: Multiply the result by 1/3 and π. V = 1051.07 ft³
Step 5: Round the result to the nearest tenth. V ≈ 1051.1 ft³
So, the volume of the cone is approximately 1051.1 cubic feet.
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