Question

Let c9 be the circle of radius 9 inches centered at the origin in the xy-coordinate system. Compute the areas of the shaded regions in the pictures below; the inner circle in the second picture is the unit circle. (Round your answers to two decimal places.)

Answer 1

To find the shaded area, subtract the area of the unit circle from the area of the larger circle.

Step-by-step explanation:

To compute the areas of the shaded regions in the pictures, we need to find the area of the larger circle (c9) and subtract the area of the smaller circle (unit circle).

The area of a circle with radius r is given by the formula A = πr^2.

So, the area of the larger circle (c9) is π * 9^2 = 81π square inches.

The area of the unit circle is π * 1^2 = π square inches.

To find the shaded area, we can subtract the area of the unit circle from the area of the larger circle: 81π - π = 80π square inches.

Rounded to two decimal places, the shaded area is approximately 251.20 square inches.