Find the dimensions of the cone of maximum volume inscribed in a sphere of radius 8 cm. [Note: Inscribed means to draw inside with the corners touching. That is, the cone is inside the sphere.]

Q: 1 1+x3

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A: Since you have posted multiple questions i can do first question as per our company guidelines…

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A: The given question has been solved in detail.

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A: The given function is: f(x,y)=x3-y3 Now,  ∇f=∂f∂x,∂f∂y=3x2,-3y2∇f(6,5)=(3(6)2,-3(5)2)=(108,-75)

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A: 4x + 5y = 10 x-1/5 = y+1/-4 = z-7 now make x in y form x-1/5 = y+1/-4 -4x +4 = 5y+5 4x =-5y -1 put…