Find the volume of a right circular cone that has a height of 3.1 in and a base with a diameter of 6.6 in. Round your answer to the nearest tenth of a cubic inch. Answer: in ^(3)

Identify Volume Formula: Identify the formula for the volume of a right circular cone. The formula for the volume (V) of a right circular cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.Calculate Base Radius: Calculate the radius of the base of the cone. The diameter of the base is given as 6.6 inches. The radius is half of the diameter, so r = diameter / 2 = 6.6 in / 2 = 3.3 in.Substitute Values: Substitute the values of the radius and height into the volume formula. Using the radius r = 3.3 inches and height h = 3.1 inches, we substitute these values into the volume formula: V = (1/3)π(3.3)^2(3.1).Calculate Volume: Calculate the volume using the substituted values. V = (1/3)π(3.3)^2(3.1) = (1/3)π(10.89)(3.1) ≈ (1/3)π(33.759) ≈ 11.253π cubic inches.Evaluate Expression: Evaluate the expression to find the volume. Using π ≈ 3.14159, we calculate the volume: V ≈ 11.253 * 3.14159 ≈ 35.342 cubic inches.Round Volume: Round the volume to the nearest tenth of a cubic inch. Rounded to the nearest tenth, the volume is approximately 35.3 cubic inches.

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Find the volume of a right circular cone that has a height of 3.1 in and a base with a diameter of 6.6 in. 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 $3$ . $1$ $\text{in}$ and a base with a diameter of $6$ . $6$ $\text{in}$ . Round your answer to the nearest tenth of a cubic inch. $\newline$ Answer: $\text{in}$ $^{3}$

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Math Problems

Grade 8

Circles: word problems

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

3

1

\text{in}

and a base with a diameter of

6

6

\text{in}

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

\newline

Answer:

\text{in}

^{3}

Identify Volume Formula: Identify the formula for the volume of a right circular cone. The formula for the volume $V$ of a right circular cone is $V = \frac{1}{3}\pi r^2 h$ , where $r$ is the radius of the base and $h$ is the height of the cone.
Calculate Base Radius: Calculate the radius of the base of the cone. $\newline$ The diameter of the base is given as $6.6$ inches. The radius is half of the diameter, so $r = \frac{\text{diameter}}{2} = \frac{6.6\,\text{in}}{2} = 3.3\,\text{in}$ .
Substitute Values: Substitute the values of the radius and height into the volume formula. $\newline$ Using the radius $r = 3.3$ inches and height $h = 3.1$ inches, we substitute these values into the volume formula: $V = (\frac{1}{3})\pi(3.3)^2(3.1)$ .
Calculate Volume: Calculate the volume using the substituted values. $\newline$ $V = \frac{1}{3}\pi(3.3)^2(3.1) = \frac{1}{3}\pi(10.89)(3.1) \approx \frac{1}{3}\pi(33.759) \approx 11.253\pi$ cubic inches.
Evaluate Expression: Evaluate the expression to find the volume. $\newline$ Using $\pi \approx 3.14159$ , we calculate the volume: $V \approx 11.253 \times 3.14159 \approx 35.342$ cubic inches.
Round Volume: Round the volume to the nearest tenth of a cubic inch. $\newline$ Rounded to the nearest tenth, the volume is approximately $35.3$ cubic inches.