Question

Four circles, each with a radius of 2 inches, are removed from a square.
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

Answer 1

Given:

Given that the radius of the circle is 2 inches.

We need to determine the area of the remaining square.

Area of a square:

Given that each circle has a radius of 2 inches.

Then, the diameter of each circle is 4 inches.

Hence, the side length of the square is 2 × 4 = 8 inches.

The area of the square is given by

$A=s^2$

$A=8^2$

$A=64$ $in^2$

Thus, the area of the square is 64 square inches.

Area of the four circles:

The area of one circle is given by

$A=\pi r^2$

Substituting r = 2, we have;

$A=4\pi$

Thus, the area of one circle is 4π in²

The area of 4 circles is 4 × 4π =16π in²

Hence, the area of the 4 circles is 16π in²

Area of the remaining square:

The area of the remaining square is given by

Area = Area of the square - Area of four circles.

Substituting the values, we get;

$Area=64-16\pi$

Thus, the area of the remaining square is (64 - 16π) in²

Hence, Option c is the correct answer.