Question

a cylinder has a volume of approximately 942.48 ft cubed. The height of the cylinder is 12 feet. What is the diameter of the cylinder?

Answer 1

To calculate the volume of a cylinder you have to use the following formula:

`V=\pi r^2h`

Where

V is the volume

r is the radius

h is the height

If we know the value of the volume and the height of the cylinder, we can calculate its radius.

First, let's write the formula in terms of r, that is, isolate r in one side of the expression and all other terms on the other side.

Pi and h are multiplying r, to cancel this multiplication you have to divide it by the same number, that is pi*h. And to keep the equality valid, what's done to one side of the equation has to be done to the other side, so divide the volume by pi*h too

`\begin{gathered} (V)/(\pi h)=(\pi hr^2)/(\pi h) \\ (V)/(\pi h)=r^2 \end{gathered}`

Next, calculate the square root to both sides of the expression to determine it for r

`\begin{gathered} \sqrt[]{(V)/(\pi h)}=\sqrt[]{r^2} \\ \sqrt[]{(V)/(\pi h)}=r \end{gathered}`

Now that we have an expression to calculate the radius, replace it with the given values of volume and height

V=942.48 ft³

h= 12ft

`\begin{gathered} r=\sqrt[]{(942.48)/(12\pi)} \\ r=5 \end{gathered}`

The radius of the cylinder is 5ft, the diameter is by definition twice the radius so

`\begin{gathered} d=r\cdot2 \\ d=5\cdot2 \\ d=10 \end{gathered}`

The diameter of the cylinder is 10ft