Question

If the height of a cylinder becomes 1/4 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.

Answer 1

Answer: (C)

Curved surface area of the cylinder will be halved.

(c) Curved surface area of the cylinder will be halved.
Let the new height and radius be h / 4 and 2 r respecitvely,
where r and h are original radius and original height of the cylinder respectively.
We know that, curved surface are of cylinder= $2\pi rh$
Then, curved surface of the new cylinder =
= 2\pi (2r) $\times \frac{1}{4}h=4\pi r\times \frac{1}{4}h=2\pi rh$
= $\frac{1}{2}\times 2\pi rh$ [multiplying and dviding by 2 ]
= $\frac{1}{2}$ original curved surface area.