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Q. How many times larger is the new volume of a cylinder if the radius is doubled and the height remains the same?

A . Volume of a Cylinder or v = Area x Height = pi x r^2 x h

where: r = original radius

h = height

When radius is doubled, New Volume or V = pi x R^2 x h

where: R = 2 x r (doubled)

V/v = R^2/r^2 = (2 x r)^2/r^2 = 4

Therefore, V = 4 x v or the new volume is 4 times the original cylinder volume after the radius is doubled

Verified answer

The radius is same and the height is doubling.

Let the radius = r

initial height, h = h

final height, h'= 2h

i) Inital Curved Surface area = 2πrh

Final Curved surface area = 2πrh' = 2πr(2h) = 4πrh

Final CSA/Initial CSA = 4πrh/2πrh = 2

So, curved Surface area becomes 2 times.

ii) Inital Total Surface area = 2πr(r+h)

Final Curved surface area = 2πr(r+h') = 2πr(r+2h)

Final CSA/Initial CSA = 2πr(r+2h)/2πr(r+h) = r+2h / r+h

So, Total Surface area becomes (r+2h)/(r+h) times.

iii) Inital Volume = πr²h

Final Volume = πr²h' = πr²(2h) = 2πr²h

Final Volume/Initial Volume = 2πr²h/πr²h = 2

So, Volume becomes 2 times.