Q239 / 270 · NDA 2017 (Phase 2) · Mathematics

A cylindrical jar without a lid has to be constructed using a given surface area of a metal sheet. If the capacity of the jar is to be maximum, then the diameter of the jar must be k times the height of the jar. The value of k is

  • A
    $1$
  • Correct answer
    B
    $2$
  • C
    $3$
  • D
    $4$

Solution

The capacity of the jar will be maximum if height and radius of the cylinder are equal. $\therefore$ height $=$ radius\ldots(i) Given diameter is k times the height of the jar. Diameter $=2 \times$ radius $=2 \times$ height \ldots(from(1)) $\therefore \mathrm{k}=2$.

Hence, the correct answer is option: 'B'.

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