Find the volume of a right circular cone that has a height of 2.1 in and a base with a diameter of 4.8 in. Round your answer to the nearest tenth of a cubic inch. Answer: in ^(3)

Find Radius of Base: To find the volume of a cone, we use the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. First, we need to find the radius of the base. The diameter is given as 4.8 inches, so the radius is half of that. Radius, r = Diameter / 2 = 4.8 inches / 2 = 2.4 inches.Plug Values into Formula: Now we can plug the values of the radius and height into the volume formula. V = (1/3)πr^2h V = (1/3)π(2.4 inches)^2(2.1 inches)Calculate Radius Squared: Next, we calculate the radius squared and then multiply by the height. (2.4 inches)^2 = 5.76 inches^2 V = (1/3)π(5.76 inches^2)(2.1 inches)Multiply Radius Squared by Height: Now we multiply 5.76 inches^2 by 2.1 inches. V = (1/3)π(5.76 inches^2 × 2.1 inches) V = (1/3)π(12.096 inches^3)Find Volume: Finally, we multiply by π and divide by 3 to find the volume. V = (1/3)π(12.096 inches^3) V ≈ (1/3)(3.14159)(12.096 inches^3) V ≈ 12.732 inches^3Round to Nearest Tenth: Now we round the volume to the nearest tenth of a cubic inch. V ≈ 12.7 inches^3

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

2

1

\text{in}

and a base with a diameter 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: To find the volume of a cone, we use the formula $V = (\frac{1}{3})\pi r^2 h$ , where $r$ is the radius of the base and $h$ is the height of the cone. First, we need to find the radius of the base. The diameter is given as $4.8$ inches, so the radius is half of that. $\newline$ Radius, $r = \text{Diameter} / 2 = 4.8 \text{ inches} / 2 = 2.4 \text{ inches}.$
Plug Values into Formula: Now we can plug the values of the radius and height into the volume formula. $\newline$ $V = \frac{1}{3}\pi r^2 h$ $\newline$ $V = \frac{1}{3}\pi (2.4 \, \text{inches})^2(2.1 \, \text{inches})$
Calculate Radius Squared: Next, we calculate the radius squared and then multiply by the height. $\newline$ $(2.4 \text{ inches})^2 = 5.76 \text{ inches}^2$ $\newline$ $V = \frac{1}{3}\pi(5.76 \text{ inches}^2)(2.1 \text{ inches})$
Multiply Radius Squared by Height: Now we multiply $5.76\,\text{inches}^2$ by $2.1\,\text{inches}$ . $\newline$ $V = \left(\frac{1}{3}\right)\pi\left(5.76\,\text{inches}^2 \times 2.1\,\text{inches}\right)$ $\newline$ $V = \left(\frac{1}{3}\right)\pi\left(12.096\,\text{inches}^3\right)$
Find Volume: Finally, we multiply by $\pi$ and divide by $3$ to find the volume. $\newline$ $V = \left(\frac{1}{3}\right)\pi(12.096 \text{ inches}^3)$ $\newline$ $V \approx \left(\frac{1}{3}\right)(3.14159)(12.096 \text{ inches}^3)$ $\newline$ $V \approx 12.732 \text{ inches}^3$
Round to Nearest Tenth: Now we round the volume to the nearest tenth of a cubic inch. $\newline$ $V \approx 12.7$ inches $^3$