Question

Find the area of the shaded region in terms of pi

Answer 1

`13(1)/(3) \pi`

Explanation:

First, find the area of the small circle whose radius is 3cm.

`A = \pi r^(2) \\A = \pi (3^(2))\\A = \pi (9)\\A = 9\pi \\`

Next, find the area of the large circle. First, you need to find the radius of the large circle by adding the 3 and 4.

Radius of large circle.

3 + 4 = 7 cm

Area of large circle:

`A = \pi r^(2) \\A = \pi (7^(2))\\A = \pi (49)\\A = 49\pi \\\\`

Now subtract the area of the small circle from the large circle since the shaded area doesn't include the small circle.

`49\pi -9\pi =40\pi`

Finally find the shaded area. To do this first find what degree of the circle is shade by dividing 120 by 360.

120/360 = 1/3

Now multiply the area by 1/3, or you can divide it by 3

`(40\pi )/(3) =13(1)/(3) \pi`