Write whether True or False and justify your answer

If the radius of a cylinder is doubled and height is halved, the volume will be doubled.


Let radius of cylinder = r

Let height of cylinder = h


Then, volume of cylinder is given by


V = πr2h …(i)


According to the question, now


Radius of the cylinder = 2r


Height of the cylinder = h/2


Then, volume of cylinder is given by


V’ = π(2r)2(h/2) = 4πr2(h/2) = 2πr2h = 2 (πr2h) = 2V


V’ = 2V


Thus, volume will be doubled if the radius of a cylinder is doubled and height is halved.


Hence, it is true.


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