Find the volume of a right circular cone that has a height of 13.7ft and a base with a circumference of 18.4ft. Round your answer to the nearest tenth of a cubic foot. Answer: ft^(3)

Find Radius of Base: First, we need to find the radius of the base of the cone. The formula for the circumference (C) of a circle is C = 2πr, where r is the radius. We can rearrange this formula to solve for r: r = C / (2π).Calculate Radius: Now, let's plug in the given circumference of 18.4 feet into the formula to find the radius. r = 18.4 ft / (2π)Use Volume Formula: Calculating the radius, we get: r ≈ 18.4 ft / (2 × 3.14159) r ≈ 18.4 ft / 6.28318 r ≈ 2.929 ftSubstitute Values: Next, we use the formula for the volume (V) of a cone, which is V = (1/3)πr^2h, where r is the radius and h is the height.Calculate Volume: We substitute the values of r and h into the volume formula: V = (1/3)π(2.929 ft)^2(13.7 ft)Round Volume: Now, we calculate the volume: V ≈ (1/3) × 3.14159 × (2.929 ft)^2 × 13.7 ft V ≈ (1/3) × 3.14159 × 8.5792 ft^2 × 13.7 ft V ≈ 122.516 ft^3Finally, we round the volume to the nearest tenth of a cubic foot: V ≈ 122.5 ft^3

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

13.7 \mathrm{ft}

and a base with a circumference of

18.4 \mathrm{ft}

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

\newline

Answer:

\mathrm{ft}^{3}

Find Radius of Base: First, we need to find the radius of the base of the cone. The formula for the circumference $C$ of a circle is $C = 2\pi r$ , where $r$ is the radius. We can rearrange this formula to solve for $r$ : $r = \frac{C}{2\pi}$ .
Calculate Radius: Now, let's plug in the given circumference of $18.4$ feet into the formula to find the radius. $\newline$ $r = \frac{18.4 \, \text{ft}}{2\pi}$
Use Volume Formula: Calculating the radius, we get: $\newline$ $r \approx 18.4 \, \text{ft} / (2 \times 3.14159)$ $\newline$ $r \approx 18.4 \, \text{ft} / 6.28318$ $\newline$ $r \approx 2.929 \, \text{ft}$
Substitute Values: Next, we use the formula for the volume $V$ of a cone, which is $V = (\frac{1}{3})\pi r^2 h$ , where $r$ is the radius and $h$ is the height.
Calculate Volume: We substitute the values of $r$ and $h$ into the volume formula: $\newline$ $V = \frac{1}{3}\pi(2.929 \text{ ft})^2(13.7 \text{ ft})$
Round Volume: Now, we calculate the volume: $\newline$ $V \approx \frac{1}{3} \times 3.14159 \times (2.929 \, \text{ft})^2 \times 13.7 \, \text{ft}$ $\newline$ $V \approx \frac{1}{3} \times 3.14159 \times 8.5792 \, \text{ft}^2 \times 13.7 \, \text{ft}$ $\newline$ $V \approx 122.516 \, \text{ft}^3$
Round Volume: Now, we calculate the volume: $\newline$ $V \approx \frac{1}{3} \times 3.14159 \times (2.929 \text{ ft})^2 \times 13.7 \text{ ft}$ $\newline$ $V \approx \frac{1}{3} \times 3.14159 \times 8.5792 \text{ ft}^2 \times 13.7 \text{ ft}$ $\newline$ $V \approx 122.516 \text{ ft}^3$ Finally, we round the volume to the nearest tenth of a cubic foot: $\newline$ $V \approx 122.5 \text{ ft}^3$