Two spheres of equal radius are taken out by cutting from a solid cube with a side of (12 + 4√3) cm. What is the maximum volume (in cm3) of each sphere?
My approach: suppose side of cube =1 and let the sphere be of unequal size with diameter D and d,
$$\sqrt3=D+d+x+y....(1 )$$ where x and y are corner distances.
$$\implies x=D/\sqrt2-D/2 $$ similarly $$y=d/\sqrt2-d/2$$
Putting in 1 and putting $$d=D$$
$$\sqrt3=2D+D\sqrt2-D=D(1+\sqrt2)$$ $$Radius =\sqrt3/2(1+\sqrt2)$$
scaling it by 12+4$\sqrt3$,
Where am i getting it wrong ?