A circle with diameter 10 centimeters is to be cut from a square of paper 10 centimeters on a side. Of the following, which is closest to the amount of paper left over after the circle is cut out?
A)9 square centimeters
B)21 square centimeters
C)24 square centimeters
D)69 square centimeters
E)84 square centimeters

Question

Quizplus · Accepted Answer

The area of the square is $10 \times 10 = 100$ square centimeters. The radius of the circle is half the diameter, so $5$ centimeters. The area of the circle is $\pi r^2 = \pi \times 5^2 = 25\pi$ square centimeters. Since $\pi$ is approximately $3.14$, the area of the circle is about $78.5$ square centimeters. Subtracting this from the area of the square gives $100 - 78.5 = 21.5$ square centimeters, which is closest to 21 square centimeters.

A Circle with Diameter 10 Centimeters Is to Be Cut