Find the volume of a right circular cone that has a height of 16.6 in and a base with a circumference of 4.8in. 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 a circle is given by the formula C = 2πr, where 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 4.8 inches: r = 4.8 in / (2π) ≈ 4.8 in / 6.2832 ≈ 0.764 inches.Use Volume Formula: Next, we can 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 of the cone.Substitute Values: Let's substitute the values of r and h into the volume formula: V = (1/3)π(0.764 in)^2(16.6 in).Calculate Volume: Now, we calculate the volume: V ≈ (1/3)π(0.583696 in^2)(16.6 in) ≈ (1/3)π(9.68815536 in^3) ≈ 3.22938512π in^3.Final Calculation: Finally, we multiply by π and round to the nearest tenth: V ≈ 3.22938512π in^3 ≈ 3.22938512 * 3.1416 in^3 ≈ 10.146 in^3 (rounded to the nearest tenth).

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Find the volume of a right circular cone that has a height of 16.6 in and a base with a circumference of
4.8in. 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 $16$ . $6$ $\text{in}$ and a base with a circumference of $4.8$ $\text{in}$ . Round your answer to the nearest tenth of a cubic inch. $\newline$ Answer: $\text{in}$ $^{3}$

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Grade 7

Convert between customary and metric systems

Full solution

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

16

6

\text{in}

and a base with a circumference of

4.8

\text{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 a circle is given by the formula $C = 2\pi r$ , where $r$ is the radius. We can rearrange this formula to solve for $r$ : $r = \frac{C}{2\pi}$ .
Calculate Radius: Now, let's calculate the radius using the given circumference of $4.8$ inches: $r = \frac{4.8 \, \text{in}}{2\pi} \approx \frac{4.8 \, \text{in}}{6.2832} \approx 0.764$ inches.
Use Volume Formula: Next, we can 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 of the cone.
Substitute Values: Let's substitute the values of $r$ and $h$ into the volume formula: $V = \frac{1}{3}\pi(0.764 \, \text{in})^2(16.6 \, \text{in})$ .
Calculate Volume: Now, we calculate the volume: V \approx \frac{$1$}{$3$}\pi(\(0. $583696$ \text{ in}^ $2$ )( $16$ . $6$ \text{ in}) \approx \frac{ $1$ }{ $3$ }\pi( $9$ . $68815536$ \text{ in}^ $3$ ) \approx $3$ . $22938512$ \pi \text{ in}^ $3$ .
Final Calculation: Finally, we multiply by $\pi$ and round to the nearest tenth: $V \approx 3.22938512\pi \, \text{in}^3 \approx 3.22938512 \times 3.1416 \, \text{in}^3 \approx 10.146 \, \text{in}^3$ (rounded to the nearest tenth).