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'.

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)

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