Question

question
find the volume of a right circular cone that has a height of 14.3 ft and a base with a diameter of 17.2 ft. round your answer to the nearest tenth of a cubic foot.
answer attempt 2 out of 2
ft³
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Explanation:

Step1: Recall cone volume formula

The volume \( V \) of a right circular cone is given by \( V = \frac{1}{3}\pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step2: Find the radius

The diameter is \( 17.2 \) ft, so the radius \( r = \frac{17.2}{2} = 8.6 \) ft.

Step3: Substitute values into formula

Substitute \( r = 8.6 \) ft and \( h = 14.3 \) ft into the formula:
\( V = \frac{1}{3} \pi (8.6)^2 (14.3) \)

Step4: Calculate the volume

First, calculate \( (8.6)^2 = 73.96 \). Then, \( 73.96 \times 14.3 = 1057.628 \). Next, \( \frac{1}{3} \times 1057.628 \approx 352.5427 \). Multiply by \( \pi \) (using \( \pi \approx 3.1416 \)): \( 352.5427 \times 3.1416 \approx 1107.9 \) (rounded to the nearest tenth).

Answer:

\( 1107.9 \)