Question

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?

Answer 1

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.