Find the volume of a right circular cone that has a height of 11.5ft and a base with a circumference of 16.5ft. Round your answer to the nearest tenth of a cubic foot. Answer: ft^(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 (11.5 ft) but not the radius. However, we are given the circumference of the base, which is 16.5 ft. We can use the circumference to find the radius with the formula C = 2πr, where C is the circumference.Calculate Radius: First, we need to solve for the radius (r) using the circumference (C = 16.5 ft). Rearrange the formula C = 2πr to r = C / (2π).Calculate Volume: Now, calculate the radius using the given circumference: r = 16.5 ft / (2π). Use π ≈ 3.14159 for the calculation.Final Volume Calculation: Perform the calculation: r = 16.5 ft / (2 * 3.14159) ≈ 16.5 ft / 6.28318 ≈ 2.625 ft. This is the radius of the base of the cone.Round to Nearest Tenth: Next, we can use the radius to find the volume of the cone using the formula V = (1/3)πr^2h. Plug in the values: r = 2.625 ft and h = 11.5 ft.Calculate the volume: V = (1/3)π(2.625 ft)^2(11.5 ft). First, calculate the radius squared: (2.625 ft)^2 ≈ 6.890625 ft^2.Now, multiply the radius squared by the height: 6.890625 ft^2 * 11.5 ft ≈ 79.2421875 ft^3.Finally, multiply by (1/3)π to get the volume: V ≈ (1/3) * 3.14159 * 79.2421875 ft^3 ≈ 83.186 ft^3.Round the answer to the nearest tenth: V ≈ 83.2 ft^3.

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Find the volume of a right circular cone that has a height of
11.5ft and a base with a circumference of
16.5ft. 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 $11.5 \mathrm{~ft}$ and a base with a circumference of $16.5 \mathrm{~ft}$ . Round your answer to the nearest tenth of a cubic foot.

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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

11.5 \mathrm{~ft}

and a base with a circumference of

16.5 \mathrm{~ft}

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

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 ( $11.5$ ft) but not the radius. However, we are given the circumference of the base, which is $16.5$ ft. We can use the circumference to find the radius with the formula $C = 2\pi r$ , where $C$ is the circumference.
Calculate Radius: First, we need to solve for the radius $r$ using the circumference $C = 16.5 \text{ ft}$ . Rearrange the formula $C = 2\pi r$ to $r = \frac{C}{2\pi}$ .
Calculate Volume: Now, calculate the radius using the given circumference: $r = \frac{16.5 \, \text{ft}}{(2\pi)}$ . Use $\pi \approx 3.14159$ for the calculation.
Final Volume Calculation: Perform the calculation: $r = \frac{16.5 \, \text{ft}}{2 \times 3.14159} \approx \frac{16.5 \, \text{ft}}{6.28318} \approx 2.625 \, \text{ft}$ . This is the radius of the base of the cone.
Round to Nearest Tenth: Next, we can use the radius to find the volume of the cone using the formula $V = \frac{1}{3}\pi r^2 h$ . Plug in the values: $r = 2.625$ ft and $h = 11.5$ ft.
Round to Nearest Tenth: Next, we can use the radius to find the volume of the cone using the formula $V = \frac{1}{3}\pi r^2h$ . Plug in the values: $r = 2.625$ ft and $h = 11.5$ ft.Calculate the volume: $V = \frac{1}{3}\pi(2.625\,\text{ft})^2(11.5\,\text{ft})$ . First, calculate the radius squared: $(2.625\,\text{ft})^2 \approx 6.890625\,\text{ft}^2$ .
Round to Nearest Tenth: Next, we can use the radius to find the volume of the cone using the formula $V = \frac{1}{3}\pi r^2 h$ . Plug in the values: $r = 2.625$ ft and $h = 11.5$ ft.Calculate the volume: $V = \frac{1}{3}\pi (2.625$ ft $)^2(11.5$ ft\). First, calculate the radius squared: $(2.625$ ft\)^ $2$ \approx $6$ . $890625$ \) ft $^2$ .Now, multiply the radius squared by the height: $6.890625$ ft $^2 \times 11.5$ ft $\approx 79.2421875$ ft $r = 2.625$ $0$ .
Round to Nearest Tenth: Next, we can use the radius to find the volume of the cone using the formula $V = \frac{1}{3}\pi r^2h$ . Plug in the values: $r = 2.625$ ft and $h = 11.5$ ft.Calculate the volume: $V = \frac{1}{3}\pi(2.625\, \text{ft})^2(11.5\, \text{ft})$ . First, calculate the radius squared: $(2.625\, \text{ft})^2 \approx 6.890625\, \text{ft}^2$ .Now, multiply the radius squared by the height: $6.890625\, \text{ft}^2 \times 11.5\, \text{ft} \approx 79.2421875\, \text{ft}^3$ .Finally, multiply by $(1/3)\pi$ to get the volume: $V \approx (1/3) \times 3.14159 \times 79.2421875\, \text{ft}^3 \approx 83.186\, \text{ft}^3$ .
Round to Nearest Tenth: Next, we can use the radius to find the volume of the cone using the formula $V = \frac{1}{3}\pi r^2h$ . Plug in the values: $r = 2.625$ ft and $h = 11.5$ ft.Calculate the volume: $V = \frac{1}{3}\pi(2.625\,\text{ft})^2(11.5\,\text{ft})$ . First, calculate the radius squared: $(2.625\,\text{ft})^2 \approx 6.890625\,\text{ft}^2$ .Now, multiply the radius squared by the height: $6.890625\,\text{ft}^2 \times 11.5\,\text{ft} \approx 79.2421875\,\text{ft}^3$ .Finally, multiply by $(1/3)\pi$ to get the volume: $V \approx (1/3) \times 3.14159 \times 79.2421875\,\text{ft}^3 \approx 83.186\,\text{ft}^3$ .Round the answer to the nearest tenth: $V \approx 83.2\,\text{ft}^3$ .