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Find the volume of a right circular cone that has a height of 14 in and a base with a radius of 9.1 in. Round your answer to the nearest tenth of a cubic inch.
Answer: in
^(3)

Find the volume of a right circular cone that has a height of $14$ $\text{in}$ and a base with a radius of $9$ . $1$ $\text{in}$ . Round your answer to the nearest tenth of a cubic inch. $\newline$ Answer: $\text{in}$ $^{3}$

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Convert between customary and metric systems

Full solution

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

14

\text{in}

and a base with a radius of

9

.

1

\text{in}

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

\newline

Answer:

\text{in}

^{3}

Identify 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.
Plug Values: Plug the given values into the formula. $\newline$ Using the given radius $r = 9.1$ inches and height $h = 14$ inches, we substitute these values into the formula to get $V = \frac{1}{3}\pi(9.1)^2(14)$ .
Calculate Volume: Calculate the volume using the given values. $\newline$ First, calculate the radius squared: $(9.1)^2 = 82.81$ . $\newline$ Then, multiply by the height: $82.81 \times 14 = 1159.34$ . $\newline$ Now, multiply by $\pi$ : $1159.34 \times \pi \approx 3641.68$ . $\newline$ Finally, multiply by $1/3$ to get the volume: $(1/3) \times 3641.68 \approx 1213.89$ .
Round Result: Round the result to the nearest tenth of a cubic inch. $\newline$ Rounding $1213.89$ to the nearest tenth gives us $1213.9$ cubic inches.

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