AP EAMCET · Maths · Application of Derivatives
Given that the solid obtained by rotating a rectangle about one of its side is a cylinder. If the perimeter of a rectangle is \(48 \mathrm{~cm}\) and the volume of the cylinder formed by rotating it is maximum, then the dimensions of that rectangle is
- A 14,10
- B 20,4
- C 18,6
- D 8,16
Answer & Solution
Correct Answer
(D) 8,16
Step-by-step Solution
Detailed explanation
Let \(l\) and \(b\) be length and width of the rectangle. \(\because\) The perimeter is \(48 \mathrm{~cm}\). \(\therefore \quad 2(l+b)=48\) \(\Rightarrow l+b=24\) ...(i) Volume of the cylinder form by rotation is \(v=\pi l^2 b\)…
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