Question 857462
Translate the description completely into symbols and see what happens.


volume of a right circular cylinder, {{{h*pi*(d/2)^2}}};
h is length top to bottom;
d is diameter
And simplifying the expression,
{{{highlight((1/4)h*pi(d^2))}}}-----for our original cylinder.


Doubling the height, which I have called "length" as h:
volume becomes {{{2h*pi*(d/2)^2}}}
Simplifying,
{{{2h*pi(d^2)/(2*2)}}}
{{{highlight((1/2)h*pi(d^2))}}}-----Cylinder when doubled height.


Starting again with original cylinder, Doubling the Diameter:
{{{h*pi(2d/2)^2}}}
Simplifying,
{{{highlight(h*pi(d^2))}}}--------Cylinder when doubled diameter.


Now you can more easily analyze how doubling the height or doubling the diameter affects the volume of the original cylinder.  You will find that each of the resulting expressions contain the same factor, {{{h*pi*d^2}}}.