Please help meee?? =[?

Question

Which increases the volume of a cylinder more, doubling the height or doubling the radius? Explain your reasoning.

Answer 1

well the formula to find out the volume for a cylinder is (pi times radius^2 times height)  since the radius is squared if you double that it will increase alot more dramatically, so doubling the radius increases it more. you can test it out on calculator too  

Answer 2

Volume of a cylinder  (V) =  ÃƒÂÃ‚€r^2h

[ That is the Surface Area of the base which is a circle = πr^2 multiplied by the height ].

When doubling the height ==> Algebrically this is = 2 * h

Then volume at 2h :

[ Substituting 2h in place of "h" in equation of volume ]

V = πr^2 ( 2h ) = 2πr^2h ==> That is 2 X the original volume

When doubling the radius ==> Algebrically this is = 2 * r

Then volume at 2r :

[ Substituting 2r in place of "r" in equation of volume ]

V = π(2r)^2h = 4πr^2h ==> That is 4 X the original volume

[ Original volume being = πr^2h ]

Hence, doubling the radius increases the volume of a cylinder more than when doubling the height and to be more specific increases it twice as more as 4πr^2h = 2 ( 2πr^2h )

Hope this helps.

Answer 3

Since the radius is squared, doubling the radius increases the volume more than doubling the height. If the height goes from 3 to 6, the volume doubles. If the radius doubles, the volume increases by a factor relative of 3 to 9.

Answer 4

If the volume of a cylinder is r^2*pi*h then doubling the height will equal r^2*pi*2*h=2r^2*h*pi

doubling the radius will equal (2r)^2*pi*h=4r^2*h*pi

doubling the radius makes the volume increase more.

Answer 5

The volume of a cylinder is V = pi*r^2*h

so let Vh be the volume of the doubled height cylinder.

Vh = pi * r^2 * (2h) = 2pir^2h

Let Vr be the volume of the doubled radius cylinder

Vr = pi * (2r)^2 * h = pi * (4r^2) * h = 4pir^2h

So you can see from the coefficient that the effect of doubling the radius is twice that of doubling the height. Or in other words

Vr = 2 * Vh

Hope that helps!

Answer 6

Doubling the radius makes the volume of a cylinder to increase because Volume of a cylinder = 22/7* r^2 * h

If the radius is doubled then it should be squared and multiplied to get the volume.

Hope this helps..............

Answer 7

Since in the formula v=pi*r²*h, radius is squared and height isn't, doubling the radius will quadruple your volume, while doubling the height will double the volume.  Example:

If you have a cylinder with radius=5 and height=12, v = pi*5²*12 = 300*pi

Double the height: v = pi*5²*24 = 600*pi

Double the radius: v = pi*10²*24 = 1200*pi