JEE Mains · Maths · STD 12 - 6. Application of derivatives
The height of a right circular cylinder of maximum volume inscribed in a sphere of radius \(3\) is
- A \(\sqrt 3\)
- B \(\sqrt 6\)
- C \(2\sqrt 3\)
- D \(\frac{2}{3} \sqrt 3\)
Answer & Solution
Correct Answer
(C) \(2\sqrt 3\)
Step-by-step Solution
Detailed explanation
\(h=2(3 \cos \theta)=6 \cos \theta,\) \( r=3 \sin \theta\) \(\mathrm{V}=\pi \mathrm{r}^{2} \mathrm{h}\) \(=\pi\left(4 \sin ^{2} \theta\right)(6 \cos \theta)\) \(=54 \pi \sin ^{2} \theta \cos \theta\) \(\frac{d v}{d \theta}=0\)…
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