Multiple choice

If the curved surface area and volume of a cylinder are $264 m^2$ and $924 m^3$ respectively, then the height of the cylinder is

  1. 6 m

  2. 6.5 m

  3. 6.7 m

  4. 6.8 m
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A Correct answer
Explanation

Curved surface area (CSA) = 2 * pi * r * h = 264. Volume (V) = pi * r^2 * h = 924. Dividing V by CSA: (pi * r^2 * h) / (2 * pi * r * h) = 924 / 264. This simplifies to r / 2 = 3.5, so r = 7. Substitute r = 7 into CSA: 2 * (22/7) * 7 * h = 264, so 44 * h = 264, h = 6.

AI explanation

The volume of a cylinder is given by the formula pi * r^2 * h, and the curved surface area is 2 * pi * r * h. Dividing the volume of 924 by the curved surface area of 264 eliminates pi, r, and h to leave r/2 = 3.5, meaning the radius r is 7 m. Plugging r back into the surface area formula gives 2 * (22/7) * 7 * h = 264, which simplifies to 44 * h = 264; therefore, the height is 6 m.

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