TS EAMCET · Maths · Application of Derivatives
The maximum volume (in cu. units) of the cylinder which can be inscribed in a sphere of radius 12 units is
- A \(384 \sqrt{3} \pi\)
- B \(768 \sqrt{3} \pi\)
- C \(\frac{768 \pi}{\sqrt{3}}\)
- D \(\frac{1152 \pi}{\sqrt{3}}\)
Answer & Solution
Correct Answer
(B) \(768 \sqrt{3} \pi\)
Step-by-step Solution
Detailed explanation
\(12^2=r^2+\left(\frac{h}{2}\right)^2\) \(\begin{aligned} & \Rightarrow V=\pi r^2 h \\ & \Rightarrow V=\pi\left(144-\frac{h^2}{4}\right) h \\ & \Rightarrow V=144 \pi h-\frac{\pi}{4} h^3 \\ & \Rightarrow \quad \frac{d V}{d h}=144 \pi-\frac{3 \pi}{4} h^2\end{aligned}\)…
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