A circle of diameter 2 inches has its center at the center of a square with 2-inch sides. Find the area of the region that is inside the square and outside the circle.
Circle area:
A = pi * r^2
A = 3.14 * 1^2
A = 3.14 sq. inches
Square area:
A = s^2
A = 2^2
A = 4 sq. inches
To find the area of the region that is inside the square and outside the circle, we need to subtract the area of the circle from the area of the square.
Step 1: Find the area of the circle
The area of a circle is given by the formula A = π*r^2, where r is the radius of the circle. In this case, the diameter is 2 inches, so the radius is half of the diameter, which is 2/2 = 1 inch.
Substituting the radius into the formula, we get A = π*(1 inch)^2 = π square inches.
Step 2: Find the area of the square
The area of a square is given by the formula A = side^2, where side is the length of one side of the square. In this case, the side length is 2 inches.
Substituting the side length into the formula, we get A = (2 inches)^2 = 4 square inches.
Step 3: Subtract the area of the circle from the area of the square
The area of the region that is inside the square and outside the circle is given by the formula A_region = A_square - A_circle.
Substituting the values we calculated, we get A_region = 4 square inches - π square inches.
Therefore, the area of the region that is inside the square and outside the circle is 4 - π square inches.