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Find the volume of a hemisphere that has a radius of 8 centimeters to the nearest tenth.

55. Find the volume of a hemisphere that has a radius of 88 centimeters to the nearest tenth.

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Full solution

Q. 55. Find the volume of a hemisphere that has a radius of 88 centimeters to the nearest tenth.
  1. Identify formula for volume: Step 11: Identify the formula for the volume of a sphere.\newlineThe formula for the volume of a sphere is V=43πr3V = \frac{4}{3}\pi r^3. Since we need the volume of a hemisphere, we take half of this volume.\newlineCalculation: Vhemisphere=12×43πr3V_{\text{hemisphere}} = \frac{1}{2} \times \frac{4}{3}\pi r^3
  2. Substitute radius into formula: Step 22: Substitute the radius into the formula.\newlineRadius r=8r = 8 cm\newlineCalculation: Vhemisphere=12×(43)π(8)3V_{\text{hemisphere}} = \frac{1}{2} \times \left(\frac{4}{3}\right)\pi(8)^3
  3. Calculate the volume: Step 33: Calculate the volume.\newlineCalculation: Vhemisphere=12×(43)π(512)V_{\text{hemisphere}} = \frac{1}{2} \times \left(\frac{4}{3}\right)\pi(512)\newline =12×(20483)π= \frac{1}{2} \times \left(\frac{2048}{3}\right)\pi\newline =10243π= \frac{1024}{3} \pi\newline =1072.5 cm3= 1072.5 \text{ cm}^3 (using π≈3.14\pi \approx 3.14)

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