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Discus: SAT/ACT Tests and Test Preparation: April 2003 Archive: SAT MATH QUESTION EMERGENCY
By Futuredoctor (Futuredoctor) on Thursday, April 24, 2003 - 10:43 pm: Edit

Hi, I just got a copy of the third edition of 10 real SAT's and in the Saturday, January 2002, there is a problem that has been stumping me...

This is a math question from section 7, #10 that says in teh figure above, a square with sides of length 6 units is divided into 9 squares. What is the area of the circle that passes through the points A, B, C, and D, which are the centers of the four corner squares.

A) 6 pi
B) 8 pi
C) 9 pi
D) 10 pi
E) 18 pi

(the diagram has a square divided into three rows and three columns. Points a, b, c, and d lie in the middle of the "corner squares")

Any help would be greatly appreciated......

By Lateralus (Lateralus) on Thursday, April 24, 2003 - 10:48 pm: Edit

The answer is 8 pi. If you draw it out, each of the smaller squares have sides of 2. The distance from the center of the entire (large) square to one of the centers of the smaller squares is the radius of the circle. This distance is 2 root 2. pi times 2 root 2 quantity squared gives you 8 pi. I hope i am correct

By Xiggi (Xiggi) on Friday, April 25, 2003 - 12:37 am: Edit

The answer is completely correct.

The only thing to add would be to make sure to visualize that the radius is also the hypothenuse of a right triangle with known sides of 2 and 2.

It may be a bit easier to say that the unknown side is Radicant 8 (root 8) instead of 2 root 2.

Then the formula is Radicant 8 squared * Pi, and radicant 8 squared is simply 8.

But again, that is just a simple variance of the correct answer posted by Lateralus.

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