Spheres

Geometry Level pending

A sphere of radius $5\text{ cm}$ is inscribed in a cube. To the nearest integer, what is the radius of the biggest sphere that can be placed in the eight corners of the cube, in the voids there?

4\text{ cm}

3\text{ cm}

2\text{ cm}

1\text{ cm}

1 solution

Nanda Kumar
May 23, 2016

Side of the cube = 10cm body diagonal = 3(^1/2)x 10cm = 17.32cm Total length of body diagonal outside the sphere = 17.32 - 10 = 7.32cm So length of free body diagonal on either side = 3.66cm Now imagine tiny cubes in each corner with this length as body diagonal and having spheres inscribed in them. So 3.66cm = 3(^1/2)x a cm, where a cm is the side of the tiny cube; so a = 3.66/ 3(^1/2) = 2.11cm This is also the diameter of the biggest sphere there. Then the radius of the biggest tiny sphere = 1.05cm

Spheres

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