Find the volume of a right circular cone that has a height of 2.5 ft and a base with a diameter of 5.2 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 2.5 ft and a base with a diameter of 5.2 ft. Round your answer to the nearest tenth of a cubic foot.
Solution
To find the volume of a right circular cone, we use the formula: V = 1/3πr²h, where r is the radius of the base, h is the height, and π is a constant approximately equal to 3.14159.
Step 1: Find the radius. The diameter of the base is given as 5.2 ft, so the radius is half of that, which is 5.2/2 = 2.6 ft.
Step 2: Substitute the values into the formula. V = 1/3 * π * (2.6 ft)² * 2.5 ft.
Step 3: Calculate the volume. V = 1/3 * 3.14159 * 6.76 ft² * 2.5 ft = 17.7 cubic ft.
So, the volume of the cone is approximately 17.7 cubic feet, rounded to the nearest tenth.
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