Question

area of a circle 2
example find the area of a circle with a radius of 6.4 ft. leave π in your answer.
$a = \pi r^{2}$
$a = \pi(6.4 ft)^{2}$
$a = \pi(40.96)$
$a = 40.96\pi ft^{2}$
directions find the areas of the circles leaving π in the answer.

1. $r = 4.3$ in.
2. $r = 2.9$ ft
3. $r = 5.1$ km
4. $r = 3.7$ cm
5. $r = 6.8$ in.
6. $r = 9.3$ m
7. $r = 8.6$ ft
8. $r = 5.5$ km
9. $r = 4.9$ m
10. $r = 3.4$ cm
11. $r = 8.1$ in.
12. $r = 7.2$ km
13. $r = 6.6$ m
14. $r = 2.8$ ft
15. $r = 1.6$ cm
16. $r = 6.1$ in.
17. $r = 9.9$ km
18. $r = 7.8$ m
19. $r = 5.3$ ft
20. $r = 4.4$ cm

Explanation:

Step1: Use 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.

Step2: Substitute the given radius into the formula

For example, for problem 1: \(r = 4.3\) in.
\(A=\pi\times(4.3)^{2}=\pi\times18.49 = 18.49\pi\) in²
For problem 2: \(r = 2.9\) ft
\(A=\pi\times(2.9)^{2}=\pi\times8.41=8.41\pi\) ft²
For problem 3: \(r = 5.1\) km
\(A=\pi\times(5.1)^{2}=\pi\times26.01 = 26.01\pi\) km²
For problem 4: \(r = 3.7\) cm
\(A=\pi\times(3.7)^{2}=\pi\times13.69=13.69\pi\) cm²
For problem 5: \(r = 6.8\) in.
\(A=\pi\times(6.8)^{2}=\pi\times46.24 = 46.24\pi\) in²
For problem 6: \(r = 9.3\) m
\(A=\pi\times(9.3)^{2}=\pi\times86.49=86.49\pi\) m²
For problem 7: \(r = 8.6\) ft
\(A=\pi\times(8.6)^{2}=\pi\times73.96 = 73.96\pi\) ft²
For problem 8: \(r = 5.5\) km
\(A=\pi\times(5.5)^{2}=\pi\times30.25=30.25\pi\) km²
For problem 9: \(r = 4.9\) m
\(A=\pi\times(4.9)^{2}=\pi\times24.01 = 24.01\pi\) m²
For problem 10: \(r = 3.4\) cm
\(A=\pi\times(3.4)^{2}=\pi\times11.56=11.56\pi\) cm²
For problem 11: \(r = 8.1\) in.
\(A=\pi\times(8.1)^{2}=\pi\times65.61 = 65.61\pi\) in²
For problem 12: \(r = 7.2\) km
\(A=\pi\times(7.2)^{2}=\pi\times51.84=51.84\pi\) km²
For problem 13: \(r = 6.6\) m
\(A=\pi\times(6.6)^{2}=\pi\times43.56 = 43.56\pi\) m²
For problem 14: \(r = 2.8\) ft
\(A=\pi\times(2.8)^{2}=\pi\times7.84=7.84\pi\) ft²
For problem 15: \(r = 1.6\) cm
\(A=\pi\times(1.6)^{2}=\pi\times2.56 = 2.56\pi\) cm²
For problem 16: \(r = 6.1\) in.
\(A=\pi\times(6.1)^{2}=\pi\times37.21=37.21\pi\) in²
For problem 17: \(r = 9.9\) km
\(A=\pi\times(9.9)^{2}=\pi\times98.01 = 98.01\pi\) km²
For problem 18: \(r = 7.8\) m
\(A=\pi\times(7.8)^{2}=\pi\times60.84=60.84\pi\) m²
For problem 19: \(r = 5.3\) ft
\(A=\pi\times(5.3)^{2}=\pi\times28.09 = 28.09\pi\) ft²
For problem 20: \(r = 4.4\) cm
\(A=\pi\times(4.4)^{2}=\pi\times19.36=19.36\pi\) cm²

Answer:

1. \(18.49\pi\) in²
2. \(8.41\pi\) ft²
3. \(26.01\pi\) km²
4. \(13.69\pi\) cm²
5. \(46.24\pi\) in²
6. \(86.49\pi\) m²
7. \(73.96\pi\) ft²
8. \(30.25\pi\) km²
9. \(24.01\pi\) m²
10. \(11.56\pi\) cm²
11. \(65.61\pi\) in²
12. \(51.84\pi\) km²
13. \(43.56\pi\) m²
14. \(7.84\pi\) ft²
15. \(2.56\pi\) cm²
16. \(37.21\pi\) in²
17. \(98.01\pi\) km²
18. \(60.84\pi\) m²
19. \(28.09\pi\) ft²
20. \(19.36\pi\) cm²