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  • Need explanation for: The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is:

The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is:

  • Option 1)

    \sqrt{6 }

  • Option 2)

    \frac{2}{3}\sqrt{3}

  • Option 3)

    2\sqrt{3}

  • Option 4)

    \sqrt{3}

Answers (1)

best_answer

radius of cylinder =\sqrt{R^{2}-\left ( \frac{h}{2} \right )^{2}}

volume of cylinder =\pi r^{2}h=\pi \left ( R^{2}-\frac{h}{4}^{2} \right )\times h

for maximum volume 

\frac{dv}{dh}=\pi \left ( R^{2}-\frac{3h}{4}^{2} \right )=0

\Rightarrow h^{2}=\frac{4R}{3}^{2}

h=2\sqrt{3}


Option 1)

\sqrt{6 }

Option 2)

\frac{2}{3}\sqrt{3}

Option 3)

2\sqrt{3}

Option 4)

\sqrt{3}

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