X and Y are two cylinders of the same height. The base of X has diameter that is half of the diameter of the base of Y. If the height of X is doubled. The volume of X becomes
equal to the volume of Y
double the volume of Y
half of the volume of Y
greater than the volume of Y
A
equal to the volume of Y
B
greater than the volume of Y
C
double the volume of Y
D
half of the volume of Y
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Solution
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For cylinder XFor cylinder Yh1=heighth2=height
d1=diameterofXd2=diameterofY
d1=d22
r1=r22
Now h1=2h2
Volume of cylinder =Basearea×height
=πr2×h
=πr2h
VxVy=πr21h1πr22h2=r22.2h24.r22.h2=12
⇒ Volume of cyhlinder C is half the volume of Y.
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