Multiple choice

The curved surface area of a cylinder is $264 m^2$ and its volume is $924 m^3$ Tile ratio of its diameter to its height is

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

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

AI explanation

Using the curved surface area formula 2*pi*r*h = 264 and the volume formula pi*r^2*h = 924, divide the volume by the curved surface area to get r/2 = 924/264. This simplifies to r/2 = 3.5, making the radius 7 m and the diameter 14 m. Substituting r = 7 into the first equation gives 2*pi*7*h = 264, so h = 264 / (14*pi), which makes h = 6 m; therefore, the ratio of diameter to height is 14:6 or 7:3.

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