If the height of a cylinder becomes1/4 of the original height and the radius is doubled, then which of the following will be true?
(a) Curved surface area of the cylinder will be doubled.
(b) Curved surface area of the cylinder will remain unchanged.
(c) Curved surface area of the cylinder will be halved.
(d) Curved surface area will be 1/4 of the original curved surface.
The correct answer is option (c) Curved surface area of the cylinder will be halved.
Explanation:
We know that the curved surface area of a cylinder with radius “r” and height “h” is given as
The curved surface area of a cylinder = 2πrh … (1)
Now, the new curved surface area of cylinder with radius 2r and height (1/4)h, then the new curved surface area is
= 2π(2r)(1/4)h
= πrh
Now, multiply an divide the new curved surface area by 2, we will get
= (1/2) (2) πrh …. (2)
Now, by comparing (1) and (2), we get:
The new curved surface area of a cylinder is (1/2) times of the original curved surface area of a cylinder.