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Find the volume of a right circular cone that has a height of
13.3ft and a base with a diameter of
9.4ft. Round your answer to the nearest tenth of a cubic foot.
Answer:
ft^(3)

Find the volume of a right circular cone that has a height of $13.3 \mathrm{ft}$ and a base with a diameter of $9.4 \mathrm{ft}$ . Round your answer to the nearest tenth of a cubic foot. $\newline$ Answer: $\mathrm{ft}^{3}$

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Circles: word problems

Full solution

Q. Find the volume of a right circular cone that has a height of

13.3 \mathrm{ft}

and a base with a diameter of

9.4 \mathrm{ft}

. Round your answer to the nearest tenth of a cubic foot.

\newline

Answer:

\mathrm{ft}^{3}

Identify Volume Formula: Identify the formula for the volume of a right circular cone. The formula for the volume $V$ of a right circular cone is $V = \frac{1}{3}\pi r^2 h$ , where $r$ is the radius of the base and $h$ is the height of the cone.
Calculate Base Radius: Calculate the radius of the base of the cone. $\newline$ The diameter of the base is given as $9.4$ feet. The radius $(r)$ is half of the diameter, so $r = \frac{\text{diameter}}{2} = \frac{9.4}{2} = 4.7$ feet.
Substitute Values: Substitute the values of the radius and height into the volume formula. $\newline$ Using the radius $r = 4.7$ feet and the height $h = 13.3$ feet, we substitute these values into the volume formula: $V = (1/3)\pi(4.7)^2(13.3)$ .
Calculate Volume: Calculate the volume using the substituted values. $\newline$ $V = \frac{1}{3}\pi(4.7)^2(13.3) = \frac{1}{3}\pi(22.09)(13.3) \approx \frac{1}{3}\pi(293.597) \approx 97.8659\pi$ cubic feet.
Evaluate Expression: Evaluate the expression to find the volume in cubic feet. Using the approximation $\pi \approx 3.14159$ , we get $V \approx 97.8659 \times 3.14159 \approx 307.454$ cubic feet.
Round Volume: Round the volume to the nearest tenth of a cubic foot. Rounded to the nearest tenth, the volume is approximately $307.5$ cubic feet.

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