Question

four circles, each with a radius of 2 inches, are removed from a square. what is the remaining area of the square? (16 - 4π) in.² (16 - π) in.² (64 - 16π) in.² (64 - 4π) in.²

Explanation:

Step1: Calculate side - length of square

The side - length of the square is equal to the sum of the diameters of two circles. Since the radius of each circle is $r = 2$ inches, the diameter $d=2r = 4$ inches. The side - length of the square $s = 4 + 4=8$ inches. The area of the square $A_{square}=s^{2}=8^{2}=64$ square inches.

Step2: Calculate total area of four circles

The area of a single circle is given by the formula $A_{circle}=\pi r^{2}$, with $r = 2$ inches. So $A_{circle}=\pi\times(2)^{2}=4\pi$ square inches. The total area of four circles $A_{total - circles}=4\times A_{circle}=4\times4\pi = 16\pi$ square inches.

Step3: Calculate remaining area

The remaining area $A = A_{square}-A_{total - circles}=64 - 16\pi$ square inches.

Answer:

$(64 - 16\pi)\text{ in.}^2$