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 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.
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For minimum material problems, express surface area in terms of one variable using volume constraint.
Updated On: Mar 19, 2026
- (2)/(3)
- (1)/(2)
- (4)/(5)
- (1)/(3)
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Verified By Collegedunia
The Correct Option is A
Solution and Explanation
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).
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