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Anon25 [30]
3 years ago
11

The volume of a cylinder is 81 cubic feet. What is the volume of a cone that fits exactly inside the cylinder? Provide an explan

ation and proof for your answer.
Mathematics
1 answer:
expeople1 [14]3 years ago
8 0
V ( cylinder ) = r² π h
V ( cone ) = 1/3 r² π h
A cone that fits exactly inside the cylinder has the volume:
V ( cone ) = 1/3 V ( cylinder = 1/3 · 81 = 27 ft³
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Answer:

\left\{\begin{array}{l}x=t\\ \\y=0\\ \\z=8\end{array}\right.

or

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Step-by-step explanation:

yz-plane has the equation x=a, where a is a real constant. The normal vector of this plane (vector perpendicular to the plane) is

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If the line is perpendicular to this plane, then it is parallel to the normal vector, so the equation of this line is

\dfrac{x-x_0}{1}=\dfrac{y-y_0}{0}=\dfrac{z-z_0}{0},

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In your case, the line is passing through the point (0,0,8), so the canonical equation of the line is

\dfrac{x-0}{1}=\dfrac{y-0}{0}=\dfrac{z-8}{0}

Write a vector parametrization for this line

\left\{\begin{array}{l}\dfrac{x-0}{1}=t\\ \\\dfrac{y-0}{0}=t\\ \\\dfrac{z-8}{0}=t\end{array}\right.\Rightarrow \left\{\begin{array}{l}x=t\\ \\y=0\\ \\z=8\end{array}\right.

3 0
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timofeeve [1]
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2 years ago
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