Multiple choice

The height and the radius of the base of a cylinder are in the ratio $3:1$. If its volume is $1029$ $ \pi\, cm^{3}$; find its total surface area.

  1. $1232$ $cm^{2}$
  2. $1200$ $cm^2$
  3. $1230$ $cm^2$
  4. $1233$ $cm^2$
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A Correct answer
Explanation

Given h/r = 3/1, so h = 3r. Volume = pi * r^2 * h = pi * r^2 * (3r) = 3 * pi * r^3 = 1029 * pi. Thus r^3 = 343, so r = 7 and h = 21. Total surface area = 2 * pi * r * (r + h) = 2 * pi * 7 * (7 + 21) = 14 * pi * 28 = 392 * pi. Using pi = 22/7, area = 392 * (22/7) = 56 * 22 = 1232.

AI explanation

Using the cylinder volume formula where the radius is r and the height is 3r, we have V = pi times r squared times h equals 1029 times pi. This yields r cubed equals 343, so the radius r is 7 cm and the height h is 21 cm. Applying the total surface area formula, 2 times pi times r times (r + h), we calculate 2 times 22 divided by 7 times 7 times 28 to get 1232 cm squared.

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