Multiple choice

Curved surface area of a cylindrical pillar is 264 $\displaystyle m^{2}$ and its volume is 924 $\displaystyle m^{3}$ The diameter of the pillar is

  1. 5 m

  2. 10 m

  3. 14 m

  4. 9 m
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C Correct answer
Explanation

The curved surface area of a cylinder is 2*pi*r*h = 264, and the volume is pi*r^2*h = 924. Dividing the volume by the surface area gives (pi*r^2*h) / (2*pi*r*h) = 924 / 264, which simplifies to r/2 = 3.5, so r = 7. The diameter is 2*r = 14 m.

AI explanation

We use the two given formulas for a cylinder: curved surface area is 2 * pi * r * h and volume is pi * r^2 * h. Dividing the volume by the curved surface area eliminates h, giving the relation (pi * r^2 * h) / (2 * pi * r * h) = r / 2. Substituting the given values of 924 and 264, we have 924 / 264 = r / 2, which simplifies to 3.5 = r / 2, meaning the radius is 7 m. The diameter is twice the radius, so it is 2 * 7 = 14 m.

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