Question

A cone has a volume of 18.84 cubic meters. The height of the cone is 2 meters. What is length ofthe radius?V=

Answer 1

Let's write out the formula for the volume of a cone,

`\text{Volume of a cone=}(1)/(3)\pi r^2h`

Let's write out the given data,

`\begin{gathered} \pi=3.14 \\ =\text{radius}=\text{?} \\ h=\text{height}=2m \\ \text{Volume}=18.84m^3 \end{gathered}`

Let's substitute our data and solve for the radius,

`\begin{gathered} 18.84=(1)/(3)*3.14* r^2*2 \\ 18.84=(1)/(3)*6.28r^2 \end{gathered}`
`\begin{gathered} \text{cross multiply} \\ 18.84*3=6.28r^2 \\ \text{Divide both sides by 6.28} \\ (18.84*3)/(6.28)=r^2 \\ 9=r^2 \\ r=\sqrt[]{9} \\ r=3m \end{gathered}`

Hence, the value for the radius is 3m.