Multiple choice

The surface area of cylindrical pipe, open at both ends is 628 sq.m. The difference between its radius and length is 15 m, the length being larger. If the pipe was closed at one end, the amount of water that it can hold is

  1. $500 \pi cu.m$
  2. $525 \pi cu.m$
  3. $550 \pi cu.m$

  4. None of these
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A Correct answer
Explanation

Surface area of open cylinder = 2 * pi * r * h = 628. Given h - r = 15, so h = r + 15. 2 * pi * r * (r + 15) = 628. Using pi = 3.14, 2 * 3.14 * r * (r + 15) = 628, so r(r + 15) = 100. r^2 + 15r - 100 = 0. (r + 20)(r - 5) = 0, so r = 5 and h = 20. Volume = pi * r^2 * h = pi * 25 * 20 = 500 * pi.

AI explanation

Use the curved surface area of an open cylinder, 2 times pi times radius times height, which gives 2 times pi times r times h equals 628 and thus r times h equals 100. Given h minus r equals 15, testing factors of 100 gives h equals 20 and r equals 5. The volume of the pipe when closed at one end is pi times r squared times h, which is pi times 25 times 20, resulting in 500 pi cubic meters.

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