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What is the volume of a hemisphere with a radius of
55.8in, rounded to the nearest tenth of a cubic inch?
Answer: in
^(3)

What is the volume of a hemisphere with a radius of $55.8$ $\mathrm{in}$ , rounded to the nearest tenth of a cubic inch? $\newline$ Answer: $\text{in}$ $^{3}$

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Convert between customary and metric systems

Full solution

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

55.8

\mathrm{in}

, rounded to the nearest tenth of a cubic inch?

\newline

Answer:

\text{in}

^{3}

Recall Sphere Volume Formula: Recall the formula for the volume of a sphere. $\newline$ The volume $V$ of a sphere is given by the formula $V = \frac{4}{3}\pi r^3$ , where $r$ is the radius of the sphere. Since a hemisphere is half of a sphere, we need to divide this volume by $2$ to get the volume of a hemisphere.
Substitute Given Radius: Substitute the given radius into the formula for the volume of a hemisphere. $\newline$ The radius $r$ is given as $55.8$ inches. So, the volume $V$ of the hemisphere is $V = \frac{1}{2} \times \frac{4}{3}\pi(55.8)^3$ .
Calculate Volume: Calculate the volume using the substituted values. $\newline$ $V = \frac{1}{2} \times \frac{4}{3}\pi(55.8)^3$ $\newline$ $V = \frac{2}{3}\pi(55.8)^3$ $\newline$ $V = \frac{2}{3}\pi(55.8 \times 55.8 \times 55.8)$ $\newline$ $V \approx \frac{2}{3}\pi(175032.152)$
Perform Multiplication and Division: Perform the multiplication and division to find the volume. $\newline$ $V \approx \frac{2}{3} \times \pi \times 175032.152$ $\newline$ $V \approx 116688.10133333333 \times \pi$ $\newline$ $V \approx 366519.4815$ cubic inches (using $\pi \approx 3.14159$ )
Round to Nearest Tenth: Round the result to the nearest tenth of a cubic inch. $\newline$ The volume of the hemisphere, rounded to the nearest tenth, is approximately $366519.5$ cubic inches.

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