Sample Question #248 (mathematics – geometry)

Wow, dude, you have a Ph.D. in math! Do me a favor, will you? My 10-year-old son was asking me this question last night but I couldn’t work it out.

A circle is inscribed in a square. What’s the ratio of the circle’s area to the square’s area?

(Comment: okay, I pose the question in a dramatic context, but this kind of question can be asked of any candidate, because everyone studied basic geometry back in elementary school!)

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ANSWER

Let r be the radius of the circle. Its area is pi*r^2. The square’s area is (2r)^2. Hence the ratio is pi/4.

The problem is more fun if the square is inscribed in a circle..

What’s the answer to that one, Stephen? 🙂

-brett