The volume of a cylinder is given by
[tex]V = A_bh[/tex]
Where [tex]A_b[/tex] is the base area and h is the height.
So, if we call [tex]V_1,\ V_2[/tex] the volumes with the original and the doubled area, we have
[tex]V_1 = A_bh,\quad V_2 = A_b(2h)[/tex]
Since the height was doubled. We deduce that
[tex]\dfrac{V_2}{V_1}=\dfrac{2A_bh}{A_bh}=2[/tex]
So, if the height is doubled, the volume will double as well.
