Friday puzzle

Trick question

> What is the area ... in square rods, rounded to the nearest square rod?

Everyone knows that if you round a square rod you end up with a dowel.

Nevertheless, the answer falls out as a nice round number. Or more precisely, the product of a round number and a 'rounder' one.

;-)

Hints

Bill has solved it, but for those still trying,

1) The statement of the problem contains data you don't need.

2) The arithmetic really is easy, once you have figured out the solution.

3) This puzzle is the two-dimension member of a family of puzzles, the 3D and 1D ones of which I have recently posted here.

Re: Friday puzzle

Must be time for a blueberry filled donut from the local Finnish deli.

Go ahead with answer

Re: Hints

While we are waiting for Bill to post is answer, I'll clarify a couple of my hints.

The length of the track and the conversion from feet to rods was included only to make the problems look hard. Neither is needed, and trying to incorporate either in your solution will bog you down.

The other problems in this "family" are the "string around the equator" problem, where the we determine the increase in the radius of a circle if the circumference is increased by a certain amount (which doesn't depend on the size of the original circle), and the volume of the portion of s sphere remaining after a 6" long hole is drilled through its center (which doesn't depend on the size of the original sphere).

Re: Go ahead with answer

As Alex said in his hint, the size of the inner circle makes no difference. The answer for the general case is the same as the answer for the degenerate case where the radius of the inner circle is zero.

The diameter of the outer circle can be calculated using the pythagorean theorem to find the hypotenuse of the right triangle formed by half of the 20 rod chord and the radius of the inner circle.

However, if you write down the equation for the area of the track, you find that everything cancels out except Pi(chord/2)^2 or 100 Pi.