Question

if the volume of the cylinder is 1500 in ^3, what is the radius of the base of the cyinder? use 3.14 for pie and round the answer to the nearest hundredth. height 12in

Answer 1

To find the volume, V, of a cylinder, the formula is

`V=\pi r^2h`

Where

`\begin{gathered} r\text{ is the radius} \\ h\text{ is the height} \end{gathered}`

Given that

`\begin{gathered} h=12in \\ \pi\text{ is taken as 3.14} \\ V=1500in^3 \end{gathered}`

To find the radius, r,

Substitute the values into to find the volume, V, of the cylinder

`\begin{gathered} V=\pi r^2h \\ 1500=3.14* r^2*12 \\ 1500=37.68r^2 \\ \text{Divide both sides by 37.68} \\ (37.68r^2)/(37.68)=(1500)/(37.68) \\ r^2=39.86393112 \\ \text{Square root of both sides} \\ \sqrt[]{r^2}=\sqrt[]{39.86393112} \\ r=6.31in\text{ (nearest hundredth)} \end{gathered}`

Hence, the radius is 6.31in (nearest hundredth)