What is the volume of a hemisphere with a diameter of 57.6m, rounded to the nearest tenth of a cubic meter? Answer: m^(3)

Calculate Radius: To find the volume of a hemisphere, we first need to find the volume of a full sphere and then divide it by 2. The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere. Since the diameter of the sphere is given as 57.6 meters, the radius r is half of the diameter. Calculation: r = diameter / 2 = 57.6m / 2 = 28.8mSubstitute Radius in Formula: Now we can substitute the radius into the formula for the volume of a sphere. Calculation: V_sphere = (4/3)π(28.8m)^3Calculate Volume of Full Sphere: We calculate the volume of the full sphere using the radius we found. Calculation: V_sphere = (4/3)π(28.8m)^3 = (4/3)π(23832.832m^3) ≈ (4/3) * 3.14159 * 23832.832m^3 ≈ 125663.706m^3Divide Volume by 2: Since we want the volume of a hemisphere, we divide the volume of the sphere by 2. Calculation: V_hemisphere = V_sphere / 2 ≈ 125663.706m^3 / 2 ≈ 62831.853m^3Round Final Volume: Finally, we round the volume of the hemisphere to the nearest tenth of a cubic meter. Calculation: V_hemisphere ≈ 62831.9m^3

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What is the volume of a hemisphere with a diameter of
57.6m, rounded to the nearest tenth of a cubic meter?
Answer:
m^(3)

What is the volume of a hemisphere with a diameter of $57.6 \mathrm{~m}$ , rounded to the nearest tenth of a cubic meter? $\newline$ Answer: $\mathrm{m}^{3}$

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Grade 7

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Full solution

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

57.6 \mathrm{~m}

, rounded to the nearest tenth of a cubic meter?

\newline

Answer:

\mathrm{m}^{3}

Calculate Radius: To find the volume of a hemisphere, we first need to find the volume of a full sphere and then divide it by $2$ . The formula for the volume of a sphere is $V = \frac{4}{3}\pi r^3$ , where $r$ is the radius of the sphere. Since the diameter of the sphere is given as $57.6$ meters, the radius $r$ is half of the diameter. $\newline$ Calculation: $r = \frac{\text{diameter}}{2} = \frac{57.6\text{m}}{2} = 28.8\text{m}$
Substitute Radius in Formula: Now we can substitute the radius into the formula for the volume of a sphere. $\newline$ Calculation: $V_{\text{sphere}} = \frac{4}{3}\pi(28.8\,\text{m})^3$
Calculate Volume of Full Sphere: We calculate the volume of the full sphere using the radius we found. $\newline$ Calculation: $V_{\text{sphere}} = \frac{4}{3}\pi(28.8\,\text{m})^3 = \frac{4}{3}\pi(23832.832\,\text{m}^3) \approx \frac{4}{3} \times 3.14159 \times 23832.832\,\text{m}^3 \approx 125663.706\,\text{m}^3$
Divide Volume by $2$ : Since we want the volume of a hemisphere, we divide the volume of the sphere by $2$ . $\newline$ Calculation: $V_{\text{hemisphere}} = \frac{V_{\text{sphere}}}{2} \approx \frac{125663.706\,\text{m}^3}{2} \approx 62831.853\,\text{m}^3$
Round Final Volume: Finally, we round the volume of the hemisphere to the nearest tenth of a cubic meter. $\newline$ Calculation: $V_{\text{hemisphere}} \approx 62831.9\,\text{m}^3$