Two spheres against a corner in a cube.
Two spheres are placed in the corner of a cube such that a cross-section shows that they are touching each other as well as the walls of the cube as shown in the figure.
If the radius of the larger sphere is R and that of the smaller sphere is r
Calculate r/R to two decimal places.
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1 solution
Distance of the center of the larger sphere from the corner
is sqrt(R^2 + R^2 + R^2) = sqrt(3)*R
Similarly the distance of the center of the smaller sphere from the corner is sqrt(3)*r.
The centres of the spheres lie on the same line which ends in the corner
so
sqrt(3) R = sqrt(3) r + r + R
ie. R(sqrt(3)-1) =r( sqrt(3) + 1)
That gives us r/R = (sqrt(3)-1)/(sqrt(3) + 1)