Question

find the exact area of each circle.
1)
2)
3)
area =
area =
area =
5)
6)
area =
area =

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius of the circle. If the diameter \(d\) is given, then \(r=\frac{d}{2}\).

Step2: Calculate the area for each circle

Circle 1:

Radius \(r = 15\) ft.
Using the formula \(A=\pi r^{2}\), we substitute \(r = 15\):
\(A=\pi\times(15)^{2}=225\pi\) square feet.

Circle 2:

Diameter \(d = 22\) in. So radius \(r=\frac{22}{2}=11\) in.
Using the formula \(A=\pi r^{2}\), we substitute \(r = 11\):
\(A=\pi\times(11)^{2}=121\pi\) square inches.

Circle 3:

Radius \(r = 9\) yd.
Using the formula \(A=\pi r^{2}\), we substitute \(r = 9\):
\(A=\pi\times(9)^{2}=81\pi\) square yards.

Circle 4:

Diameter \(d = 12\) yd. So radius \(r=\frac{12}{2}=6\) yd.
Using the formula \(A=\pi r^{2}\), we substitute \(r = 6\):
\(A=\pi\times(6)^{2}=36\pi\) square yards.

Circle 5:

Radius \(r = 3\) in.
Using the formula \(A=\pi r^{2}\), we substitute \(r = 3\):
\(A=\pi\times(3)^{2}=9\pi\) square inches.

Circle 6:

Diameter \(d = 34\) ft. So radius \(r=\frac{34}{2}=17\) ft.
Using the formula \(A=\pi r^{2}\), we substitute \(r = 17\):
\(A=\pi\times(17)^{2}=289\pi\) square feet.

Answer:

1. \(225\pi\) square feet
2. \(121\pi\) square inches
3. \(81\pi\) square yards
4. \(36\pi\) square yards
5. \(9\pi\) square inches
6. \(289\pi\) square feet