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requireo Find the volume of a hemisphere with a great circle circumference of 37.7 centimeters.

Find the volume of a hemisphere with a great circle circumference of 37.737.7 centimeters.

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Full solution

Q. Find the volume of a hemisphere with a great circle circumference of 37.737.7 centimeters.
  1. Calculate Circle Radius: Step 11: Calculate the radius of the circle using the circumference formula.\newlineCircumference formula: C=2πrC = 2\pi r\newlineGiven C=37.7 cmC = 37.7\,\text{cm}, solve for rr:\newline37.7=2πr37.7 = 2\pi r\newliner=37.72πr = \frac{37.7}{2\pi}\newliner≈37.76.28r \approx \frac{37.7}{6.28}\newliner≈6.0 cmr \approx 6.0\,\text{cm}
  2. Calculate Hemisphere Volume: Step 22: Calculate the volume of the hemisphere using the volume formula.\newlineVolume of a hemisphere formula: V=23πr3V = \frac{2}{3}\pi r^3\newlineSubstitute r=6.0r = 6.0 cm:\newlineV=23π(6.0)3V = \frac{2}{3}\pi(6.0)^3\newlineV=23π(216)V = \frac{2}{3}\pi(216)\newlineV≈23×3.14×216V \approx \frac{2}{3} \times 3.14 \times 216\newlineV≈452.16V \approx 452.16 cm3^3

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