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Find the volume of a right circular cone that has a height of 19 ft and a base with a diameter of 18.7 ft. Round your answer to the nearest tenth of a cubic foot.
To find the volume of a right circular cone, we use the formula:
V = (1/3) * π * r^2 * h
Given that the height (h) is 19 ft and the base has a diameter of 18.7 ft, we can find the radius (r) using half of the diameter:
r = 18.7 ft / 2 = 9.35 ft
Substituting the values into the formula:
V = (1/3) * π * (9.35 ft)^2 * 19 ft
V = (1/3) * π * 87.4225 ft^2 * 19 ft
V ≈ (0.333) * 3.14159 * 1660.4163 ft^3
V ≈ 1740.4535 ft^3
Rounding to the nearest tenth of a cubic foot:
V ≈ 1740.5 ft^3
Therefore, the volume of the right circular cone is approximately 1740.5 cubic feet.