Multiple choice

A square sheet of side $28$ cm is folded into a cylinder by joining its two sides. Find the base area of the cylinder thus formed (in $\displaystyle cm^{2}$).

  1. $\displaystyle \frac{524}{11}$
  2. $\displaystyle \frac{575}{11}$
  3. $\displaystyle \frac{629}{11}$
  4. $\displaystyle \frac{686}{11}$
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D Correct answer
Explanation

Circumference of cylinder base = 28. 2 * pi * r = 28, so r = 14 / pi. Base area = pi * r^2 = pi * (14/pi)^2 = 196 / pi. Using pi = 22/7, area = 196 * 7 / 22 = 1372 / 22 = 686 / 11.

AI explanation

By rolling the square sheet into a cylinder, the side length of 28 cm becomes the base circumference, so 2(pi)r = 28, yielding a radius of 14/22 cm. The base area formula is (pi)(r^2), which is calculated as (22/7) times (14/22)^2, equaling 686/11 square cm.

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