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```
find the radius R of the largest sphere that can be fitted into a cylinder of radius 'r' and height 'h' in terms of 'r' and 'h'.

```
9 years ago

```							Dear student,
R=radius  of  sphere     x=  the  hight of  the cylinder  r=radius  of  cylinder  r^2+x^2=(2R)^2      r^2=-x^2+4R^2  v(x)=pi*r^2*h=pi(-x^2+4R^2)*x=pi*(-x^3…   v'=pi(-3x^2+4R^2)=0    3x^2=4R^2  x^2=4R^2/3     r^2=-x^2+4R^2=-4R^2/3+4R^2=4R^2*2/3=  8R^2/3    r=sqrt(8R^2/3 )=Rsqrt(8/3)

All the best.
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Sagar Singh
B.Tech, IIT Delhi

```
9 years ago
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