Find the volume of a right circular cone that has a height of 13.4m and a base with a circumference of 13.6m. Round your answer to the nearest tenth of a cubic meter. Answer: m^(3)

Find Radius from Circumference: To find the volume of a cone, we need to know the radius of the base and the height. The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height. We are given the height (13.4m) but only the circumference of the base (13.6m), not the radius. We can find the radius by using the formula for the circumference of a circle, which is C = 2πr.Calculate Radius: First, we need to solve for the radius (r) using the circumference (C = 13.6m). The formula for circumference is C = 2πr, so we can rearrange it to solve for r: r = C / (2π).Calculate Volume with Radius: Now, let's calculate the radius: r = 13.6m / (2π). We can approximate π as 3.14159.Calculate Volume with Formula: Performing the calculation gives us r = 13.6m / (2 * 3.14159) ≈ 13.6m / 6.28318 ≈ 2.165m.Round Final Volume: With the radius found, we can now calculate the volume of the cone using the formula V = (1/3)πr^2h. Plugging in the values, we get V = (1/3) * π * (2.165m)^2 * 13.4m.Calculating the volume gives us V = (1/3) * 3.14159 * (2.165m)^2 * 13.4m ≈ (1/3) * 3.14159 * 4.690225m^2 * 13.4m.Performing the multiplication, we get V ≈ (1/3) * 3.14159 * 62.849015m^3 ≈ 65.973m^3.Finally, we round the volume to the nearest tenth of a cubic meter, which gives us V ≈ 66.0m^3.

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Find the volume of a right circular cone that has a height of
13.4m and a base with a circumference of
13.6m. Round your answer to the nearest tenth of a cubic meter.
Answer:
m^(3)

Find the volume of a right circular cone that has a height of $13.4 \mathrm{~m}$ and a base with a circumference of $13.6 \mathrm{~m}$ . Round your answer to the nearest tenth of a cubic meter. $\newline$ Answer: $\mathrm{m}^{3}$

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Grade 7

Convert between customary and metric systems

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

13.4 \mathrm{~m}

and a base with a circumference of

13.6 \mathrm{~m}

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

\newline

Answer:

\mathrm{m}^{3}

Find Radius from Circumference: To find the volume of a cone, we need to know the radius of the base and the height. The formula for the volume of a cone is $V = (\frac{1}{3})\pi r^2 h$ , where $r$ is the radius and $h$ is the height. We are given the height ( $13.4$ m) but only the circumference of the base ( $13.6$ m), not the radius. We can find the radius by using the formula for the circumference of a circle, which is $C = 2\pi r$ .
Calculate Radius: First, we need to solve for the radius $r$ using the circumference $C = 13.6\,\text{m}$ . The formula for circumference is $C = 2\pi r$ , so we can rearrange it to solve for $r$ : $r = \frac{C}{2\pi}$ .
Calculate Volume with Radius: Now, let's calculate the radius: $r = \frac{13.6\,\text{m}}{2\pi}$ . We can approximate $\pi$ as $3.14159$ .
Calculate Volume with Formula: Performing the calculation gives us $r = \frac{13.6\,\text{m}}{2 \times 3.14159} \approx \frac{13.6\,\text{m}}{6.28318} \approx 2.165\,\text{m}$ .
Round Final Volume: With the radius found, we can now calculate the volume of the cone using the formula $V = \frac{1}{3}\pi r^2 h$ . Plugging in the values, we get $V = \frac{1}{3} \times \pi \times (2.165\,\text{m})^2 \times 13.4\,\text{m}$ .
Round Final Volume: With the radius found, we can now calculate the volume of the cone using the formula $V = \frac{1}{3}\pi r^2h$ . Plugging in the values, we get $V = \frac{1}{3} \times \pi \times (2.165\,\text{m})^2 \times 13.4\,\text{m}$ .Calculating the volume gives us $V = \frac{1}{3} \times 3.14159 \times (2.165\,\text{m})^2 \times 13.4\,\text{m} \approx \frac{1}{3} \times 3.14159 \times 4.690225\,\text{m}^2 \times 13.4\,\text{m}$ .
Round Final Volume: With the radius found, we can now calculate the volume of the cone using the formula $V = \frac{1}{3}\pi r^2h$ . Plugging in the values, we get $V = \frac{1}{3} \times \pi \times (2.165\,\text{m})^2 \times 13.4\,\text{m}$ . Calculating the volume gives us $V = \frac{1}{3} \times 3.14159 \times (2.165\,\text{m})^2 \times 13.4\,\text{m} \approx \frac{1}{3} \times 3.14159 \times 4.690225\,\text{m}^2 \times 13.4\,\text{m}$ . Performing the multiplication, we get $V \approx \frac{1}{3} \times 3.14159 \times 62.849015\,\text{m}^3 \approx 65.973\,\text{m}^3$ .
Round Final Volume: With the radius found, we can now calculate the volume of the cone using the formula $V = \frac{1}{3}\pi r^2h$ . Plugging in the values, we get $V = \frac{1}{3} \times \pi \times (2.165\,\text{m})^2 \times 13.4\,\text{m}$ . Calculating the volume gives us $V = \frac{1}{3} \times 3.14159 \times (2.165\,\text{m})^2 \times 13.4\,\text{m} \approx \frac{1}{3} \times 3.14159 \times 4.690225\,\text{m}^2 \times 13.4\,\text{m}$ . Performing the multiplication, we get $V \approx \frac{1}{3} \times 3.14159 \times 62.849015\,\text{m}^3 \approx 65.973\,\text{m}^3$ . Finally, we round the volume to the nearest tenth of a cubic meter, which gives us $V \approx 66.0\,\text{m}^3$ .