Problem Solving

A circular mat with diameter 20 inches is placed on a square tabletop, each of whose
sides is 24 inches long. Which of the following is closest to the fraction of the tabletop
covered by the mat?

A. 5/12
B. 2/5
C. 1/2
D. 3/4
E. 5/6

approx 1/2: C

area of circle = 10*10*3.14 = 314

area of square = 24*24

fraction = 314/24*24

314 is approx. equal to 312 (312 is div by both 3 @ 4)

312/24 = 13
13/24 = approx 1/2

Diameter of the mat is 20, so that means that its radius is 10, so its surface will be 10*10*Pi=100Pi. The surface of the table top will be 24*24. The fraction of the tabletop covered by the mat will be 10*10*Pi/24*24 = 5*5*Pi/12*12. We can approximate Pi with 3 so the fraction would be around 25/48. Since 2*12 = 24, 4*12 = 48, and 2*12/4*12 = 24/48 = 1/2, I would approximate the whole thing with 1/2.

Answer: C