Multiple choice

The curved surface area and volume of a cylindrical pillar are $264 m^2$ and $924 m^{3}$. Find the ratio of its diameter to its height.

  1. $3 : 7$
  2. $7 : 3$
  3. $6 : 7$
  4. $7 : 6$
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B Correct answer
Explanation

CSA = 2 * pi * r * h = 264. Volume = pi * r^2 * h = 924. Dividing V by CSA: (pi * r^2 * h) / (2 * pi * r * h) = r / 2 = 924 / 264 = 3.5. So r = 7. Then 2 * pi * 7 * h = 264 => h = 264 / (44) = 6. Diameter = 14, height = 6. Ratio 14:6 = 7:3.

AI explanation

Divide the volume 924 by the curved surface area 264 to get the radius, which is 3.5 m. Use the curved surface area formula 2 times pi times r times h equals 264 to find the height, so 2 times 22 over 7 times 3.5 times h equals 264, giving h equals 12 m. The diameter is twice the radius, which is 7 m, making the ratio of diameter to height 7 : 3.

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