AP EAMCET · Maths · Application of Derivatives
A closed cylinder of given volume will have least surface area when the ratio of its height and base radius is
- A
- B
- C
- D
Answer & Solution
Correct Answer
(A)
Step-by-step Solution
Detailed explanation
For a closed cylinder let the height be h and base radius be r. Volume, V=πr2h i.e. h=Vπr2 Now, surface area, S=2πrh+2πr2=2πrVπr2+2πr2 =2Vr+2πr2 For least surface area, dSdr=0 ⇒-2Vr2+4πr=0⇒V=2πr3 Hence,…
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