Question

if the ratio of radii of two cylinders of same height is 4:5, then show that the ratio of their curved surface areas 4:5 and the ratio of their volumes is 16:25

Answer 1

hello friend , here is your answer ,

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let the radii of both the cylinders be 4r and 5r respectively . and height be h

curved surface area of smaller cylinder = 2×π×4r×h
=8πrh

curved surface area of larger cylinder=2×π×5r×h=10πrh

ratio of CSA = 8πrh:10πrh
= 8:10
= 4:5

volume of smaller cylinder = π(4r)²h
=16πr²h

volume of bigger cylinder = π(5r)²h
=25πr²h

ratio of volumes = 16πr²h:25πr²h
=16:25

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