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

Question

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 1

True

Justification:

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.

New radius of the cylinder, R = 2r

New curved surface area of the cylinder, CSA’ = 2πrh …(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 get,

Since, 2πrh ≠ 4πrh

equation (i) ≠ equation (ii)

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

Then,

CSA’ = 2π(2r)(h/2) = 2πrh

Hence, the given statement “If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved” is true.