Get Answers to all your Questions

header-bg qa

  The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius=\sqrt{3}  is :

  • Option 1)

    \frac{4}{3}\sqrt{3}\pi

  • Option 2)

    \frac{8}{3}\sqrt{3}\pi

  • Option 3)

    4\pi

  • Option 4)

    2\pi

 

Answers (1)

best_answer

As we have learned

Method for maxima or minima -

By second derivative method :

Step\:1.\:\:find\:values\:of\:x\:for\:\frac{dy}{dx}=0

Step\:\:2.\:\:\:x=x_{\circ }\:\:is\:a\:point\:of\:local\:maximum\:if  f''(x)<0\:\:and\:local\:minimum\:if\:f''(x)>0

- wherein

Where\:\:y=f(x)

\frac{dy}{dx}=f'(x)

 

 vol . of cylinder = \pi r^2( h ^ 2 / 4 )

\Rightarrow 3 = r^2 + \frac{h^2 }{4 }

\Rightarrow h^2 = 4 (3- r^2)\\ \Rightarrow r^2 = 3 - (h^2 /4 )

V = \pi h (3- \frac{h^2 }{4 }) \\ = 3 \pi h - \frac{\pi }{4}h^3 \\ \Rightarrow \frac{dv}{dh} = 3 \pi - \frac{3 \pi }{4 }h^2 \\ \Rightarrow h = 2

 

\therefore volume = \pi \times 2 \times (3-1)= 4 \pi

 

 

 

 

 

 

 


Option 1)

\frac{4}{3}\sqrt{3}\pi

Option 2)

\frac{8}{3}\sqrt{3}\pi

Option 3)

4\pi

Option 4)

2\pi

Posted by

Himanshu

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE