What is the volume of a hemisphere with a diameter of $52.5 \mathrm{ft}$ , rounded to the nearest tenth of a cubic foot? $\newline$ Answer: $\mathrm{ft}^{3}$

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

52.5 \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. Given the diameter of the sphere is $52.5$ feet, we can find the radius by dividing the diameter by $2$ .
Calculate Volume of Full Sphere: Calculate the radius of the sphere. The radius $r$ is half of the diameter, so $r = \frac{\text{diameter}}{2} = \frac{52.5\text{ft}}{2} = 26.25\text{ft}$ .
Calculate Numerical Value: Now, we can calculate the volume of the full sphere using the formula $V = \frac{4}{3}\pi r^3$ . Substituting the value of $r = 26.25$ ft, we get $V = \frac{4}{3}\pi (26.25\text{ft})^3$ .
Divide Volume by $2$ : Perform the calculation for the volume of the full sphere. $V = \left(\frac{4}{3}\right)\pi(26.25\,\text{ft})^3 = \left(\frac{4}{3}\right)\pi(26.25\,\text{ft} \times 26.25\,\text{ft} \times 26.25\,\text{ft})$ .
Calculate Final Volume: Calculate the numerical value for the volume of the full sphere. $V = \frac{4}{3}\pi(26.25\,\text{ft} \times 26.25\,\text{ft} \times 26.25\,\text{ft}) \approx \frac{4}{3}\pi(18150.625\,\text{ft}^3) \approx \frac{4}{3} \times \pi \times 18150.625\,\text{ft}^3 \approx 24134.375\pi\,\text{ft}^3$ .
Calculate Numerical Value: To find the volume of the hemisphere, divide the volume of the full sphere by $2$ . $V_{\text{hemisphere}} = \frac{V_{\text{sphere}}}{2} \approx \frac{(24134.375\pi \text{ft}^3)}{2} \approx 12067.1875\pi \text{ft}^3$ .
Perform Final Calculation: Now, we need to calculate the numerical value for the volume of the hemisphere. Using the approximation $\pi \approx 3.14159$ , we get $V_{\text{hemisphere}} \approx 12067.1875 \times 3.14159\,\text{ft}^3$ .
Round Volume: Perform the final calculation for the volume of the hemisphere. $V_{\text{hemisphere}} \approx 12067.1875 \times 3.14159\,\text{ft}^3 \approx 37909.511\,\text{ft}^3$ .
Round Volume: Perform the final calculation for the volume of the hemisphere. $V_{\text{hemisphere}} \approx 12067.1875 \times 3.14159\,\text{ft}^3 \approx 37909.511\,\text{ft}^3$ .Round the volume of the hemisphere to the nearest tenth of a cubic foot. The rounded volume is approximately $37909.5\,\text{ft}^3$ .