What is the volume of a hemisphere with a radius of 4.9ft, rounded to the nearest tenth of a cubic foot? Answer: ft^(3)

Identify formula for volume: Identify the formula for the volume of a sphere, since a hemisphere is half of a sphere. The formula for the volume of a sphere is V = (4/3)πr^3.Calculate full sphere volume: Calculate the volume of a full sphere using the given radius of 4.9ft. V_sphere = (4/3)π(4.9)^3Perform calculation for sphere volume: Perform the calculation for the volume of the full sphere. V_sphere = (4/3)π(4.9)^3 = (4/3)π(117.649)Calculate numerical value: Calculate the numerical value for the volume of the full sphere. V_sphere ≈ (4/3) * 3.14159 * 117.649 ≈ 490.875 cubic feetDivide volume for hemisphere: Since we need the volume of a hemisphere, we divide the volume of the sphere by 2. V_hemisphere = V_sphere / 2 V_hemisphere ≈ 490.875 / 2Calculate hemisphere volume: Calculate the volume of the hemisphere. V_hemisphere ≈ 245.4375 cubic feetRound volume to nearest tenth: Round the volume of the hemisphere to the nearest tenth of a cubic foot. V_hemisphere_rounded ≈ 245.4 cubic feet

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What is the volume of a hemisphere with a radius of
4.9ft, rounded to the nearest tenth of a cubic foot?
Answer:
ft^(3)

What is the volume of a hemisphere with a radius of $4.9 \mathrm{ft}$ , rounded to the nearest tenth of a cubic foot? $\newline$ Answer: $\mathrm{ft}^{3}$

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Math Problems

Grade 7

Convert between customary and metric systems

Full solution

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

4.9 \mathrm{ft}

, rounded to the nearest tenth of a cubic foot?

\newline

Answer:

\mathrm{ft}^{3}

Identify formula for volume: Identify the formula for the volume of a sphere, since a hemisphere is half of a sphere. $\newline$ The formula for the volume of a sphere is $V = \frac{4}{3}\pi r^3$ .
Calculate full sphere volume: Calculate the volume of a full sphere using the given radius of $4.9\text{ft}$ . $\newline$ $V_{\text{sphere}} = \frac{4}{3}\pi(4.9)^3$
Perform calculation for sphere volume: Perform the calculation for the volume of the full sphere. $V_{\text{sphere}} = \left(\frac{4}{3}\right)\pi(4.9)^3 = \left(\frac{4}{3}\right)\pi(117.649)$
Calculate numerical value: Calculate the numerical value for the volume of the full sphere. $V_{\text{sphere}} \approx \left(\frac{4}{3}\right) \times 3.14159 \times 117.649 \approx 490.875$ cubic feet
Divide volume for hemisphere: Since we need the volume of a hemisphere, we divide the volume of the sphere by $2$ . $\newline$ $V_{\text{hemisphere}} = \frac{V_{\text{sphere}}}{2}$ $\newline$ $V_{\text{hemisphere}} \approx \frac{490.875}{2}$
Calculate hemisphere volume: Calculate the volume of the hemisphere. $V_{\text{hemisphere}} \approx 245.4375$ cubic feet
Round volume to nearest tenth: Round the volume of the hemisphere to the nearest tenth of a cubic foot. $\newline$ $V_{\text{hemisphere rounded}} \approx 245.4$ cubic feet