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,

$\text{Volume of a cone=}\frac{1}{3}\pi r^2h$

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=\frac{1}{3}\times3.14\times r^2\times2 \\ 18.84=\frac{1}{3}\times6.28r^2 \end{gathered}$$\begin{gathered} \text{cross multiply} \\ 18.84\times3=6.28r^2 \\ \text{Divide both sides by 6.28} \\ \frac{18.84\times3}{6.28}=r^2 \\ 9=r^2 \\ r=\sqrt[]{9} \\ r=3m \end{gathered}$

Hence, the value for the radius is 3m.