Question

If a cylinder has a height of 7 inches and avolume of 2,908.33 ins, find its diameter.

Answer 1

Remember that the formula for the volume of a cylinder is:

`V=\pi r^2h`

We know that:

`r=(D)/(2)`

Thereby,

`V=\pi r^2h\rightarrow V=\pi((D)/(2))^2h\rightarrow V=(\pi D^2h)/(4)`

Solving for D,

`\begin{gathered} V=(\pi D^2h)/(4)\rightarrow4V=\pi D^2h\rightarrow(4V)/(\pi h)=D^2 \\ \rightarrow D=\sqrt[]{(4V)/(\pi h)} \end{gathered}`

Using the data given,

`\begin{gathered} D=\sqrt[]{(4V)/(\pi h)} \\ \\ \Rightarrow D=23 \end{gathered}`

We get that the diameter of the cylinder is 23"