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May 16, 2020

Surface Area Problem | TOMATO BStat Objective 725

Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Surface Area.

Surface Area Problem (B.Stat Objective Question )

A right circular cylindrical container closed on both sides is to contain a fixed volume of motor oil. Suppose its base has diameter d and height is h. The overall surface area of the container is minimum when

  • h=\(\frac{4d\pi}{3}\)
  • h=d
  • h=2d
  • conditions other than the foregoing are satisfied

Key Concepts


Area and Volume


Check the Answer


B.Stat Objective Problem 725

Challenges and Thrills of Pre-College Mathematics by University Press

Try with Hints

First hint


or,\( \frac{4V}{h\pi}=d^{2}\)

or, \(d=\sqrt{\frac{4V}{h\pi}}\) positive value taken



Second Hint

for minimum surface area


or, \(\frac{2V}{h^{2}}\)=\(\frac{\sqrt{4V\pi}}{2\sqrt{h}}\)

or, \(h^{\frac{3}{2}}=2\sqrt{\frac{V}{\pi}}\)

or, \(h^{3}=\frac{4V}{\pi}\)

Final Step

or,\(h^{3}=\frac{4V}{\pi}\) where \(V=\frac{hd^{2}\pi}{4}\)


or, \(h^{2}=d^{2}\)

or, h=d (since h,d both positive)

is required answer.

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