The volume (V) of a sphere is given by the formula

Mathematics

1 answer:

Julli [10]2 years ago

8 0

V=4pi*r^3 /3 volume of sphere

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3 years ago

A hemisphere has an area of 256 pi cm^2. What is its volume?

Amanda [17]

$\bf \begin{array}{llll}
\textit{surface area of a sphere}\\\\
A=4\pi r^2
\\\\\\
\textit{a hemisphere is half that}\\\\
A=\cfrac{4\pi r^2}{2}\implies A=2\pi r^2
\end{array}\qquad r=radius
\\\\\\
\textit{now, we know the area is }256\pi \implies 256\pi =2\pi r^2
\\\\\\
\cfrac{256\pi }{2\pi }=r^2\implies \sqrt{128}=r\implies \boxed{8\sqrt{2}=r}
\\\\
-----------------------------\\\\$

$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4}{3}\pi r^3\qquad r=radius
\\\\\\
\textit{a hemisphere is half that}\\\\
V=\cfrac{\frac{4}{3}\pi r^3}{2}\implies V=\cfrac{\frac{4\pi r^3}{3}}{\frac{2}{1}}\implies V=\cfrac{4\pi r^3}{3}\cdot \cfrac{1}{2}
\\\\\\
V=\cfrac{2\pi r^3}{3}
\\\\\\
\textit{now, we know the radius is }8\sqrt{2}\implies V=\cfrac{2\pi (8\sqrt{2})^3}{3}
\\\\\\
V=\cfrac{2\pi (8^3\sqrt{2^3})}{3}\implies V=\cfrac{2\pi \cdot 512\cdot 2\sqrt{2}}{3}
\\\\\\
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