Question

Calculate r and a relationship from the following figure. All spheres are of equal radius r.

If r = x * a, round off x to 2 decimals and type 100x.

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Answer 1

Did you try to calculate using the circles on the side of the square?

You can't do that because they are not touching each other. We don't know how much the remaining edge of the square is.

So what we have to do is this: we have to join the circles along the diagonal of the square and then equate that to 2r.

So, $\sqrt{2a}$ = 4r

⇒ a = $2\sqrt{2r}$

⇒ r = 0.35a

We had r = x * a

Comparing ⇒ x = 0.35

⇒ 100x = 35