Four circles, each with a radius of 2 inches, are removed
from a square. What is the remaining area of the square?

Exact answer = 64 - 16pi

Approximate answer = 13.7345175425633

Units for the area are in square inches.

Work Shown:

The radius of each circle is 2 inches. Double this value to get the diameter to be 4 inches.

Two circles along the top have their diameters combine to 8 inches total, which is the side length of the square.

The area of the entire square, before we subtract off the circles, is 8^2 = 64 square inches.

Let A = 64

The area of one circle is pi*r^2 = pi*2^2 = 4pi square inches. Four circles combine to an area of 4*4pi = 16pi square inches.

Let B = 16pi

Subtract A and B to get the area of the shaded region, which is the leftover area after subtracting off the four circles

A-B = 64-16pi

To get the approximate answer, use a calculator

64-16pi = 13.7345175425633

step-by-step explanation:

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