Q. 44.3( 4 Votes )

Write whether True or False and justify your answer

If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved.

Answer :

Let radius of the cylinder = r

Height of the cylinder = h


Then, curved surface area of the cylinder, CSA = 2πrh


According to the question, radius is doubled and curved surface area is not changed. We can write as,


New radius of the cylinder (say, R) = 2r


& new curved surface area of the cylinder, CSA’ = 2πrh [i.e., unchanged] …(i)


Alternate case: when R = 2r and CSA’ = 2πrh


But curved surface area of cylinder in this case, CSA’= 2πRh = 2π(2r)h = 4πrh …(ii)


Comparing equations (i) and (ii), we can say


equation (i) ≠ equation (ii)


as 2πrh ≠ 4πrh


Thus, if h = h/2 (height is halved) then,


CSA’ = 2π(2r)(h/2) = 2πrh


It matched CSA’ in equation (i).


Hence, it is true.


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