Question

The volume of a cone of height 9cm is 1848cm^3. find its radius. Take π=22/7

Answer 1

SOLUTION

The formula to calculate the volume(V) of a cone is,

$V=\frac{1}{3}\pi r^2h$

Given:

$\begin{gathered} V=1848cm^3 \\ \pi=\frac{22}{7} \\ h=9cm \\ r=\text{?} \end{gathered}$

Isolate for the radius 'r' in the equation of the volume

$\begin{gathered} V\times3=\pi r^2h \\ \frac{3V}{\pi h}=\frac{\pi r^2h}{\pi h} \\ \frac{3V}{\pi h}=r^2 \\ \therefore r=\sqrt[]{\frac{3V}{\pi h}} \end{gathered}$

Substitute the values for V, h, and pi and solve for r

$\begin{gathered} r=\sqrt[]{\frac{3\times1848}{\frac{22}{7}\times9}}=\sqrt{196}=14 \\ \therefore r=14cm \end{gathered}$

Hence, the answer is 14cm.