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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 $37.7$ centimeters.

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Find the radius or diameter of a circle

Full solution

Q. Find the volume of a hemisphere with a great circle circumference of

37.7

centimeters.

Calculate Circle Radius: Step $1$ : Calculate the radius of the circle using the circumference formula. $\newline$ Circumference formula: $C = 2\pi r$ $\newline$ Given $C = 37.7\,\text{cm}$ , solve for $r$ : $\newline$ $37.7 = 2\pi r$ $\newline$ $r = \frac{37.7}{2\pi}$ $\newline$ $r \approx \frac{37.7}{6.28}$ $\newline$ $r \approx 6.0\,\text{cm}$
Calculate Hemisphere Volume: Step $2$ : Calculate the volume of the hemisphere using the volume formula. $\newline$ Volume of a hemisphere formula: $V = \frac{2}{3}\pi r^3$ $\newline$ Substitute $r = 6.0$ cm: $\newline$ $V = \frac{2}{3}\pi(6.0)^3$ $\newline$ $V = \frac{2}{3}\pi(216)$ $\newline$ $V \approx \frac{2}{3} \times 3.14 \times 216$ $\newline$ $V \approx 452.16$ cm $^3$

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