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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?
Option C is the correct answer.
Area of circle=πr^2=π10^2 ≈ 314 (d=20 –> r=10);
Area of square= (24)^2=576;
Area of circle/ area of square=314/576=157/288.
Now this fraction is obviously between 1/2 and 3/4 –> 1/2=144/288 and 3/4=216/288 — > 157 is closer to 144 than to 216.