What is the volume of a hemisphere with a diameter of 7.4ft, rounded to the nearest tenth of a cubic foot? Answer: ft^(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 is given as 7.4 feet, the radius r is half of the diameter.Volume Formula for Sphere: Calculate the radius of the sphere by dividing the diameter by 2. Radius r = Diameter / 2 = 7.4ft / 2 = 3.7ftCalculate Full Sphere Volume: Now, plug the radius into the volume formula for a sphere. V_sphere = (4/3)π(3.7ft)^3Calculate Hemisphere Volume: Calculate the volume of the full sphere using the radius. V_sphere = (4/3)π(3.7ft)^3 = (4/3)π(50.653ft^3) ≈ (4/3) * 3.1416 * 50.653ft^3 ≈ 67.020ft^3Round Final Result: Since we want the volume of a hemisphere, we divide the volume of the sphere by 2. V_hemisphere = V_sphere / 2 ≈ 67.020ft^3 / 2 ≈ 33.510ft^3Round the result to the nearest tenth of a cubic foot. V_hemisphere ≈ 33.5ft^3

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What is the volume of a hemisphere with a diameter of
7.4ft, rounded to the nearest tenth of a cubic foot?
Answer:
ft^(3)

What is the volume of a hemisphere with a diameter of $7.4 \mathrm{ft}$ , rounded to the nearest tenth of a cubic foot? $\newline$ Answer: $\mathrm{ft}^{3}$

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Grade 7

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Full solution

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

7.4 \mathrm{ft}

, rounded to the nearest tenth of a cubic foot?

\newline

Answer:

\mathrm{ft}^{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 is given as $7.4$ feet, the radius $r$ is half of the diameter.
Volume Formula for Sphere: Calculate the radius of the sphere by dividing the diameter by $2$ . $\newline$ Radius $r = \frac{\text{Diameter}}{2} = \frac{7.4\,\text{ft}}{2} = 3.7\,\text{ft}$
Calculate Full Sphere Volume: Now, plug the radius into the volume formula for a sphere. $V_{\text{sphere}} = \left(\frac{4}{3}\right)\pi(3.7\,\text{ft})^3$
Calculate Hemisphere Volume: Calculate the volume of the full sphere using the radius. $V_{\text{sphere}} = \frac{4}{3}\pi(3.7\text{ft})^3 = \frac{4}{3}\pi(50.653\text{ft}^3) \approx \frac{4}{3} \times 3.1416 \times 50.653\text{ft}^3 \approx 67.020\text{ft}^3$
Round Final Result: Since we want the volume of a hemisphere, we divide the volume of the sphere by $2$ . $\newline$ $V_{\text{hemisphere}} = \frac{V_{\text{sphere}}}{2} \approx \frac{67.020\,\text{ft}^3}{2} \approx 33.510\,\text{ft}^3$
Round Final Result: Since we want the volume of a hemisphere, we divide the volume of the sphere by $2$ . $\newline$ $V_{\text{hemisphere}} = \frac{V_{\text{sphere}}}{2} \approx \frac{67.020\,\text{ft}^3}{2} \approx 33.510\,\text{ft}^3$ Round the result to the nearest tenth of a cubic foot. $\newline$ $V_{\text{hemisphere}} \approx 33.5\,\text{ft}^3$