Help step by step pls.

Mathematics

1 answer:

Archy [21]3 years ago

8 0

Using the law of sines, we have

$\dfrac{\sin B}{2x-24}=\dfrac{\sin C}{x-2}$

but angles B and C are congruent, so the sine terms cancel and we're left with

$\dfrac1{2x-24}=\dfrac1{x-2}\implies2x-24=x-2\implies x=22$

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$\bf \begin{array}{llll}
\textit{surface area of a sphere}\\\\
A=4\pi r^2
\\\\\\
\textit{a hemisphere is half that}\\\\
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\end{array}\qquad r=radius
\\\\\\
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-----------------------------\\\\$

$\bf \textit{volume of a sphere}\\\\
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\\\\\\
\textit{a hemisphere is half that}\\\\
V=\cfrac{\frac{4}{3}\pi r^3}{2}\implies V=\cfrac{\frac{4\pi r^3}{3}}{\frac{2}{1}}\implies V=\cfrac{4\pi r^3}{3}\cdot \cfrac{1}{2}
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\boxed{V=\cfrac{2048\pi \sqrt{2}}{3}}$

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