Find the volume of a right circular cone that has a height of 19.8ft and a base with a circumference of 3.5ft. 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 of a circle is C = 2πr, where C is the circumference and r is the radius. We can rearrange this formula to solve for r: r = C / (2π).Calculate Radius: Now, let's calculate the radius using the given circumference of 3.5 feet: r = 3.5 ft / (2π). We can approximate π as 3.14159.Volume Formula: Performing the calculation: r = 3.5 ft / (2 * 3.14159) ≈ 3.5 ft / 6.28318 ≈ 0.557 ft.Substitute Values: Next, we use the formula for the volume of a cone, which is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.Calculate Volume: Substitute the values of r and h into the volume formula: V = (1/3)π(0.557 ft)^2(19.8 ft).Perform Multiplication: Calculate the volume: V ≈ (1/3) * 3.14159 * (0.557 ft)^2 * 19.8 ft ≈ (1/3) * 3.14159 * 0.310249 ft^2 * 19.8 ft.Round Answer: Perform the multiplication: V ≈ (1/3) * 3.14159 * 0.310249 ft^2 * 19.8 ft ≈ 3.14159 * 0.103416 ft^2 * 19.8 ft ≈ 6.437 ft^3.Finally, we round the answer to the nearest tenth of a cubic foot: V ≈ 6.4 ft^3.

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Find the volume of a right circular cone that has a height of
19.8ft and a base with a circumference of
3.5ft. 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 $19.8 \mathrm{ft}$ and a base with a circumference of $3.5 \mathrm{ft}$ . Round your answer to the nearest tenth of a cubic foot. $\newline$ Answer: $\mathrm{ft}^{3}$

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Convert between customary and metric systems

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

19.8 \mathrm{ft}

and a base with a circumference of

3.5 \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 of a circle is $C = 2\pi r$ , where $C$ is the circumference and $r$ is the radius. We can rearrange this formula to solve for $r$ : $r = \frac{C}{2\pi}$ .
Calculate Radius: Now, let's calculate the radius using the given circumference of $3.5$ feet: $r = \frac{3.5 \, \text{ft}}{2\pi}$ . We can approximate $\pi$ as $3.14159$ .
Volume Formula: Performing the calculation: $r = \frac{3.5 \, \text{ft}}{2 \times 3.14159} \approx \frac{3.5 \, \text{ft}}{6.28318} \approx 0.557 \, \text{ft}.$
Substitute Values: Next, we use the formula for the volume of a cone, which is $V = (\frac{1}{3})\pi r^2 h$ , where $V$ is the volume, $r$ is the radius, and $h$ is the height.
Calculate Volume: Substitute the values of $r$ and $h$ into the volume formula: $V = \frac{1}{3}\pi(0.557 \text{ ft})^2(19.8 \text{ ft})$ .
Perform Multiplication: Calculate the volume: $V \approx \frac{1}{3} \times 3.14159 \times (0.557 \text{ ft})^2 \times 19.8 \text{ ft} \approx \frac{1}{3} \times 3.14159 \times 0.310249 \text{ ft}^2 \times 19.8 \text{ ft}$ .
Round Answer: Perform the multiplication: $V \approx (\frac{1}{3}) \times 3.14159 \times 0.310249 \text{ ft}^2 \times 19.8 \text{ ft} \approx 3.14159 \times 0.103416 \text{ ft}^2 \times 19.8 \text{ ft} \approx 6.437 \text{ ft}^3$ .
Round Answer: Perform the multiplication: $V \approx (1/3) \times 3.14159 \times 0.310249 \text{ ft}^2 \times 19.8 \text{ ft} \approx 3.14159 \times 0.103416 \text{ ft}^2 \times 19.8 \text{ ft} \approx 6.437 \text{ ft}^3$ . Finally, we round the answer to the nearest tenth of a cubic foot: $V \approx 6.4 \text{ ft}^3$ .