If the radius of the base of a right circular cylinder is halved, keeping theheight same, find the ratio of thevolume of the reduced cylinder to that of theoriginal cylinder.
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Let R, H, V be the original radius, height & volume of the cylinder respectively.
and let r, h, v be the current radius, height & volume of the cylinder respectively.
As given R=2r and H=h
Volume of cylinder =pi×r²×h,
V=pi×R²×H and v=pi×r²×H
Ratio of volumes = V/v
Ratio=(pi×R²×H) / (pi×r²×H)
Ratio=R²/r²
Ratio=(2r)²/r²
Ratio=4r²/r²
Ratio=4/1
Original volume:Current volume = 4:1
Reduced cyl volume:Original cyl volume = 1:4
and let r, h, v be the current radius, height & volume of the cylinder respectively.
As given R=2r and H=h
Volume of cylinder =pi×r²×h,
V=pi×R²×H and v=pi×r²×H
Ratio of volumes = V/v
Ratio=(pi×R²×H) / (pi×r²×H)
Ratio=R²/r²
Ratio=(2r)²/r²
Ratio=4r²/r²
Ratio=4/1
Original volume:Current volume = 4:1
Reduced cyl volume:Original cyl volume = 1:4
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