What is the volume of a hemisphere with a radius of 7.1ft, rounded to the nearest tenth of a cubic foot? Answer: ft^(3)

Recall Sphere Volume Formula: Recall the formula for the volume of a sphere. The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. Since a hemisphere is half of a sphere, we need to divide the volume of a sphere by 2 to get the volume of a hemisphere.Calculate Sphere Volume: Calculate the volume of a sphere with a radius of 7.1ft. Using the formula V = (4/3)πr^3, we substitute r with 7.1ft. V = (4/3)π(7.1)^3Evaluate Sphere Volume: Evaluate the expression to find the volume of the sphere. V = (4/3)π(7.1)^3 = (4/3)π(357.911) Now, calculate the numerical value using π ≈ 3.14159. V ≈ (4/3) * 3.14159 * 357.911 V ≈ 4 * 3.14159 * 89.47775 V ≈ 12.56636 * 89.47775 V ≈ 1125.664Divide by 2 for Hemisphere: Divide the volume of the sphere by 2 to get the volume of the hemisphere. Since a hemisphere is half of a sphere, we take the volume calculated in Step 3 and divide it by 2. Volume of hemisphere = 1125.664 / 2 Volume of hemisphere ≈ 562.832Round Hemisphere Volume: Round the volume of the hemisphere to the nearest tenth of a cubic foot. 562.832 rounded to the nearest tenth is 562.8.

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What is the volume of a hemisphere with a radius of
7.1ft, rounded to the nearest tenth of a cubic foot?
Answer:
ft^(3)

What is the volume of a hemisphere with a radius of $7.1 \mathrm{ft}$ , rounded to the nearest tenth of a cubic foot? $\newline$ Answer: $\mathrm{ft}^{3}$

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Grade 7

Convert between customary and metric systems

Full solution

Q. What is the volume of a hemisphere with a radius of

7.1 \mathrm{ft}

, rounded to the nearest tenth of a cubic foot?

\newline

Answer:

\mathrm{ft}^{3}

Recall Sphere Volume Formula: Recall the formula for the volume of a sphere. $\newline$ The volume of a sphere is given by the formula $V = \frac{4}{3}\pi r^3$ , where $r$ is the radius of the sphere. Since a hemisphere is half of a sphere, we need to divide the volume of a sphere by $2$ to get the volume of a hemisphere.
Calculate Sphere Volume: Calculate the volume of a sphere with a radius of $7.1\text{ft}$ . Using the formula $V = \frac{4}{3}\pi r^3$ , we substitute $r$ with $7.1\text{ft}$ . $V = \frac{4}{3}\pi(7.1)^3$
Evaluate Sphere Volume: Evaluate the expression to find the volume of the sphere. $\newline$ $V = \frac{4}{3}\pi(7.1)^3 = \frac{4}{3}\pi(357.911)$ $\newline$ Now, calculate the numerical value using $\pi \approx 3.14159$ . $\newline$ $V \approx \frac{4}{3} \times 3.14159 \times 357.911$ $\newline$ $V \approx 4 \times 3.14159 \times 89.47775$ $\newline$ $V \approx 12.56636 \times 89.47775$ $\newline$ $V \approx 1125.664$
Divide by $2$ for Hemisphere: Divide the volume of the sphere by $2$ to get the volume of the hemisphere. $\newline$ Since a hemisphere is half of a sphere, we take the volume calculated in Step $3$ and divide it by $2$ . $\newline$ Volume of hemisphere $= 1125.664 / 2$ $\newline$ Volume of hemisphere $\approx 562.832$
Round Hemisphere Volume: Round the volume of the hemisphere to the nearest tenth of a cubic foot. $562.832$ rounded to the nearest tenth is $562.8$ .