Question

Find the relation between r and a in the following figure.

if a = x $\ast$ r , type 100x rounded off to 2 decimal places.

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Answer 1

Notice that we have 3 spheres along the diagonal of the cube.

So, we can be certain that the diameter of the spheres lies along the diagonal of the cube.

So, 2d = diagonal of cube = $\sqrt{3a}$

So, 4r = $\sqrt{3a}$

Now, a = $\frac{4}{\sqrt{3}}$ $\ast$ r = 2.30 $\ast$ r

So my x is 2.30 and multiplied by 100 is 230.