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

$\dfrac{V_2}{V_1}=\dfrac{2A_bh}{A_bh}=2$

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