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3 years ago

The diameter of the base of the cone measures 8 units. The height measures 6 units. What is the volume of the cone?

1 answer:

8 0

The volume of the cone will be given by:
volume,v=1/3πr^2h
radius,r=8/2=4 units
height,h=6 units
thus;
v=1/3*π*4^2*6
v=32π cubic units

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$\begin{gathered} P^n_r=\frac{n!}{(n-r)!} \\ \end{gathered}$

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$\begin{gathered} C^n_r=\frac{n!}{(n-r)!r!} \\ \\ \end{gathered}$

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Number of permuations:

$\begin{gathered} P^8_6=\frac{8!}{(8-6)!} \\ =\frac{8!}{2!}=\frac{8\times7\times6\times5\times4\times3\times2!}{2!} \\ 2!\text{ cancel out, thus we have} \\ \begin{equation*} 8\times7\times6\times5\times4\times3 \end{equation*} \\ \Rightarrow P_6^8=20160 \end{gathered}$

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$\begin{gathered} C^8_6=\frac{8!}{(8-6)!6!} \\ =\frac{8!}{2!\times6!}=\frac{8\times7\times6!}{6!\times2\times1} \\ 6!\text{ cancel out, thus we have} \\ \frac{8\times7}{2} \\ \Rightarrow C_6^8=28 \end{gathered}$

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