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Find the volume of a right circular cone that has a height of 11.8ft and a base with a radius of 7.3ft. Round your answer to the nearest tenth of a cubic foot.

Find the volume of a right circular cone that has a height of 11.8ft11.8ft and a base with a radius of 7.3ft7.3ft. Round your answer to the nearest tenth of a cubic foot.

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Full solution

Q. Find the volume of a right circular cone that has a height of 11.8ft11.8ft and a base with a radius of 7.3ft7.3ft. Round your answer to the nearest tenth of a cubic foot.
  1. Recall Formula: Recall the formula for the volume of a cone.\newlineThe volume VV of a cone is given by the formula V=13πr2hV = \frac{1}{3}\pi r^2 h, where rr is the radius of the base and hh is the height of the cone.
  2. Plug in Values: Plug in the given values into the formula.\newlineHere, r=7.3r = 7.3 ft and h=11.8h = 11.8 ft. So, V=13π(7.3)2(11.8)V = \frac{1}{3}\pi(7.3)^2(11.8).
  3. Calculate Radius Squared: Calculate the radius squared.\newline(7.3)2=53.29(7.3)^2 = 53.29.
  4. Multiply Radius and Height: Multiply the radius squared by the height. 53.29×11.8=628.82253.29 \times 11.8 = 628.822.
  5. Multiply by (1/3)π(1/3)\pi: Multiply the result by (1/3)π(1/3)\pi.(1/3)π×628.822≈3.14159/3×628.822≈658.037(1/3)\pi \times 628.822 \approx 3.14159/3 \times 628.822 \approx 658.037.
  6. Round to Nearest Tenth: Round the result to the nearest tenth. 658.037658.037 rounded to the nearest tenth is 658.0658.0 ft³.

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