Question

A cone with a radius of 6 cm and a height of 8 cm has the same volume as a cylinder with a height of 6 cm. What is the radius

Answer 1

Answer:

The radius of the cylinder is 4 cm.

Step-by-step explanation:

Given:

radius of cone = 6 cm

height of the cone = 8 cm

height of cylinder = 6 cm

We need to find the radius of cylinder.

Solution:

First we will find the volume of cone.

Volume of cone is one third time square of radius times height times π.

framing in equation form we get;

Volume of cone = $\frac{1}{3}\pi r^2h = \frac{1}{3}\pi\times 6^2\times 8 \approx 301.44 \ cm^3$

Now Volume of cylinder is given by square of radius times height times π.

framing in equation form we get;

Volume of cylinder = $\pi r^2h=18.84r^2$

Now it has been given that;

Volume of cone is equal to Volume of cylinder.

so we can say that

$18.84r^2=301.44$

Dividing both side by 18.84 we get;

$\frac{18.84r^2}{18.84}=\frac{301.84}{18.84}\\\\r^2\approx16$

Taking square root on both side we get;

$\sqrt{r^2}=\sqrt{16} \\\\r=4\ cm$

Hence the radius of the cylinder is 4 cm.