Question

A cone has a radius of r units and a height of h units. a cylinder has a ridius of 2r units and has the same volume as the cone. What is the height of the cylinder? write and explanation of how you got your answer.

Answer 1

Volume of a cone is calculated as:

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

Volume of the cylinder is calculated as:

$V_{cylinder}= \pi R^{2}H$

The radius of cylinder is twice the radius of cone. So R=2r. The two volumes are given to be equal, so we can write:

$\frac{1}{3} \pi r^{2} h= \pi R^{2} H \\ \\ \frac{1}{3} r^{2} h= (2r)^{2} H \\ \\ \frac{1}{3} r^{2} h= 4r^{2} H \\ \\ \frac{1}{3} h= 4H \\ \\ H= \frac{1}{12}h$ 

Thus, the height of the cylinder will be h/12

Answer 2

volume of the cone=1/3(pi r^2)(h)and volume of the cylinder= piR^2H
So the radius is equal to 2r
let H be the height
So we will just equate the two volumes:1/3(pi r^2)(h)=piR^2H1/3(pi r^2)(h=(2r)^2H1/3(pi r^2)(h=4r^2H1/3h=4HH=1/12h
SO the height is 1/12h