Solutions

Question

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?

 

Difficulty Level

Medium

Solution

Option C is the correct answer.

Option Analysis

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.