Find the volume of a right circular cone that has a height of 11.2 in and a base with a circumference of 12.6 in. Round your answer to the nearest tenth of a cubic inch. Answer: in ^(3)

Find Radius of Base: Find the radius of the base of the cone using the circumference. 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). Given that the circumference is 12.6 inches, we can calculate the radius as follows: r = 12.6 in / (2π).Calculate Radius: Calculate the radius. r = 12.6 in / (2 * 3.14159). r ≈ 12.6 in / 6.28318. r ≈ 2.0054 in. We will round this to the nearest tenth at the end of the calculation.Use Volume Formula: 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. We already found r ≈ 2.0054 in and we are given h = 11.2 in. Now we can plug these values into the formula to find the volume. V ≈ (1/3)π(2.0054 in)^2(11.2 in).Calculate Volume: Calculate the volume. V ≈ (1/3) * 3.14159 * (2.0054 in)^2 * 11.2 in. V ≈ (1/3) * 3.14159 * 4.0217 in^2 * 11.2 in. V ≈ 0.33333 * 3.14159 * 4.0217 in^2 * 11.2 in. V ≈ 47.1239 in^3.Round Volume: Round the volume to the nearest tenth of a cubic inch. V ≈ 47.1 in^3.

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

11

2

\text{in}

and a base with a circumference of

12

6

\text{in}

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

\newline

Answer:

\text{in}

^{3}

Find Radius of Base: Find the radius of the base of the cone using the circumference. $\newline$ The formula for the circumference $C$ of a circle is $C = 2\pi r$ , where $r$ is the radius. $\newline$ We can rearrange this formula to solve for $r$ : $r = \frac{C}{2\pi}$ . $\newline$ Given that the circumference is $12.6$ inches, we can calculate the radius as follows: $\newline$ $r = \frac{12.6 \, \text{in}}{2\pi}$ .
Calculate Radius: Calculate the radius. $\newline$ $r = \frac{12.6 \, \text{in}}{2 \times 3.14159}$ . $\newline$ $r \approx \frac{12.6 \, \text{in}}{6.28318}$ . $\newline$ $r \approx 2.0054 \, \text{in}$ . $\newline$ We will round this to the nearest tenth at the end of the calculation.
Use Volume Formula: 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. $\newline$ We already found $r \approx 2.0054$ in and we are given $h = 11.2$ in. $\newline$ Now we can plug these values into the formula to find the volume. $\newline$ $V \approx \frac{1}{3}\pi(2.0054\,\text{in})^2(11.2\,\text{in})$ .
Calculate Volume: Calculate the volume. $\newline$ $V \approx (\frac{1}{3}) \times 3.14159 \times (2.0054 \, \text{in})^2 \times 11.2 \, \text{in}.$ $\newline$ $V \approx (\frac{1}{3}) \times 3.14159 \times 4.0217 \, \text{in}^2 \times 11.2 \, \text{in}.$ $\newline$ $V \approx 0.33333 \times 3.14159 \times 4.0217 \, \text{in}^2 \times 11.2 \, \text{in}.$ $\newline$ $V \approx 47.1239 \, \text{in}^3.$
Round Volume: Round the volume to the nearest tenth of a cubic inch. $V \approx 47.1$ in $^3$ .