Find the volume of a right circular cone that has a height of 15.5 in and a base with a circumference of 16.8in. Round your answer to the nearest tenth of a cubic inch. Answer: in ^(3)

Find Radius of Base: First, we need to find the radius of the base of the cone. We know the circumference (C) of the base is given by C = 2 * π * r, where r is the radius. We can rearrange this formula to solve for r: r = C / (2 * π).Calculate Radius: Now, let's calculate the radius using the given circumference of 16.8 inches: r = 16.8 in / (2 * π). We can approximate π as 3.14159.Use Volume Formula: Performing the calculation for the radius: r = 16.8 in / (2 * 3.14159) ≈ 16.8 in / 6.28318 ≈ 2.675 in.Substitute Values: Next, we need to use the formula for the volume of a cone, which is V = (1/3) * π * 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 = (1/3) * π * (2.675 in)^2 * 15.5 in.Continue Calculation: Calculate the volume: V = (1/3) * 3.14159 * (2.675 in)^2 * 15.5 in ≈ (1/3) * 3.14159 * 7.156625 in^2 * 15.5 in.Finish Calculation: Continue the calculation: V ≈ (1/3) * 3.14159 * 111.02890625 in^3 * 15.5 in ≈ 3.14159 * 37.0096354167 in^3 * 15.5 in.Round Volume: Finish the calculation: V ≈ 3.14159 * 573.649449583 in^3 ≈ 1809.557 in^3.Finally, we round the volume to the nearest tenth: V ≈ 1809.6 in^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

15

5

\text{in}

and a base with a circumference of

16.8

\mathrm{in}

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

\newline

Answer:

\text{in}

^{3}

Find Radius of Base: First, we need to find the radius of the base of the cone. We know the circumference $C$ of the base is given by $C = 2 \cdot \pi \cdot r$ , where $r$ is the radius. We can rearrange this formula to solve for $r$ : $r = \frac{C}{2 \cdot \pi}$ .
Calculate Radius: Now, let's calculate the radius using the given circumference of $16.8$ inches: $r = \frac{16.8 \, \text{in}}{2 \cdot \pi}$ . We can approximate $\pi$ as $3.14159$ .
Use Volume Formula: Performing the calculation for the radius: $r = \frac{16.8 \, \text{in}}{(2 \times 3.14159)} \approx \frac{16.8 \, \text{in}}{6.28318} \approx 2.675 \, \text{in}.$
Substitute Values: Next, we need to 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: $V = \frac{1}{3} \pi (2.675 \, \text{in})^2 \times 15.5 \, \text{in}$ .
Continue Calculation: Calculate the volume: $V = \frac{1}{3} \times 3.14159 \times (2.675 \, \text{in})^2 \times 15.5 \, \text{in} \approx \frac{1}{3} \times 3.14159 \times 7.156625 \, \text{in}^2 \times 15.5 \, \text{in}.$
Finish Calculation: Continue the calculation: $V \approx (\frac{1}{3}) \times 3.14159 \times 111.02890625 \, \text{in}^3 \times 15.5 \, \text{in} \approx 3.14159 \times 37.0096354167 \, \text{in}^3 \times 15.5 \, \text{in}.$
Round Volume: Finish the calculation: $V \approx 3.14159 \times 573.649449583$ in $^3 \approx 1809.557$ in $^3$ .
Round Volume: Finish the calculation: $V \approx 3.14159 \times 573.649449583$ in $^3$ $\approx 1809.557$ in $^3$ .Finally, we round the volume to the nearest tenth: $V \approx 1809.6$ in $^3$ .