Question

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 ratio of the radius to the height of the cylinder using minimum material for the same capacity.

• A. (2)/(3)
• B. (1)/(2)
• C. (4)/(5)
• D. (1)/(3)

Hint:

For minimum material problems, express surface area in terms of one variable using volume constraint.

Answer 1

The Correct Option is A

Let radius =r, height =h. Step 1: Volume fixed: V=π r²h Step 2: Material used: M=2π rh + (5)/(4)π r² Step 3: Using h=(V)/(π r²) and minimizing M w.r.t. r, we obtain: (r)/(h)=(2)/(3) Hence, required ratio is (2)/(3).