Question

find the area of the shaded region. use the approximation 3.14 for π.
the area of the shaded region is approximately
(simplify your answer. type a whole number or a decimal.)
(diagram: square with an inscribed circle, diameter of circle is 18 in.)

Explanation:

Step1: Find area of square

The side length of the square is equal to the diameter of the circle, which is 18 in. The area of a square is side length squared, so $A_{square} = 18^2 = 324$ square inches.

Step2: Find area of circle

The radius of the circle is half of the diameter, so $r = \frac{18}{2} = 9$ in. The area of a circle is $\pi r^2$, using $\pi \approx 3.14$, so $A_{circle} = 3.14 \times 9^2 = 3.14 \times 81 = 254.34$ square inches.

Step3: Find area of shaded region

The shaded region is the area of the square minus the area of the circle, so $A_{shaded} = A_{square} - A_{circle} = 324 - 254.34 = 69.66$ square inches.

Answer:

69.66