Multiple choice

A cylindrical gas container is closed at the top and open at the bottom; if the iron plate of the top is $5/4$ times as thick as the plate forming the cylindrical sides, find the radio of the radius to the height of the cylinder using minimum material for the same capacity.

  1. $\dfrac{5}{4}$
  2. $\dfrac{4}{5}$
  3. $\dfrac{5}{2}$
  4. $\dfrac{2}{5}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

With fixed volume, h is proportional to 1/r^2. Minimizing the weighted material area, (5/4)pi r^2 + 2pi rh, gives h = 5r/4. Therefore, r/h = 4/5.

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