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What is one possible set of dimensions of a cone that has the same volume as a cylinder with a radius of 2 inches and a height of 4 inches?

User Hugsbrugs
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1 Answer

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The volume of a cone is given by the following formula:


Vcone=(\pi r^2h)/(3)

And the volume of a cylinder is given by the following formula:


Vcy=\pi r^2h

Where r is the radius and h is the height of the figure.

In this case, we are asked to find a set of dimensions for a cone so its volume equals the volume of a cylinder, then we can formulate the following expression:


\begin{gathered} Vcone=Vcy \\ (\pi r^2h)/(3)=\pi r^2h \end{gathered}

Let's assume that the radius of the cone equals 2, as the radius of the cylinder, then by replacing 4 for the height of the cylinder and 2 for the radius of both the cone and the cylinder, we get:


\begin{gathered} (\pi2^2h)/(3)=\pi2^24 \\ \frac{\pi*4*^{}h}{3}=\pi4*4 \end{gathered}

As you can see, we have 4π on both sides of this equation, by dividing the expression by 4π we can get rid of this factor, to get:


(h)/(3)=4

By multiplying both sides by 3, we get the height of the cone:


h=4*3=12

Then, a possible set of dimensions of a cone that has the same volume as the cylinder is a radius of 2 inches and a height of 12 inches.

User TridenT
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