If the height of a cylinder becomes 18 of the original height and the radius is doubled, then which of the following will be true?
Volume of the cylinder will be halved
Let us assume the height and radius of the original cylinder as h and r respectively.
Let V1 be the original volume and V2 be the volume after the change in height and radius.
Therefore volume of the original cylinder is given by: V=πr2h
height of a cylinder becomes 18of the original height and the radius is doubled
We have,r2=2r and h2=h8
So the new volume is given by:
V2=πr22h2=π(2r)2(h8)
⇒V2=4πr2h8
⇒V2=πr2h2=V12
⇒V2=V12
Hence the correct answer is Option C