Question

Mr. Kelly's company manufactures a cylindrical soup can that has a diameter of 6 inches and a volume of 226 cubic inches. If the diameter stays the same and the height is doubled, what will happen to the can's volume?​

Answer 1

The volume of a cylinder is given by

`V = A_bh`

Where
`A_b` is the base area and h is the height.

So, if we call
`V_1,\ V_2` the volumes with the original and the doubled area, we have

`V_1 = A_bh,\quad V_2 = A_b(2h)`

Since the height was doubled. We deduce that

`(V_2)/(V_1)=(2A_bh)/(A_bh)=2`

So, if the height is doubled, the volume will double as well.