10.
(2 points) Construct the altitude from point A.

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xcji7384

16.04.2023

Mathematics

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 7 &,& 2~) 
% (c,d)
&&(~ 5 &,& 4~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-2}{5-7}\implies \cfrac{2}{-2}\implies -1$

since the sphere has a diameter of 20, its radius is half that, or 10.

$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}~~
\begin{cases}
r=radius\\
-----\\
r=10
\end{cases}\implies V=\cfrac{4\pi (10)^3}{3}$

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10. (2 points) Construct the altitude from point A.