Question

practice 8-4 circumference and area of circles
find the circumference and area of each circle to the nearest tenth.
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given the circumference of a circle, find the radius to the nearest tenth.

1. $c = 80$ km
2. $c = 92$ ft
3. $c = 420$ in.
4. $c = 700$ km
5. the radius of the large circle is 8 in.

the radius of each of the smaller circles is 1 in. find the area of the shaded region to the nearest unit.

Explanation:

1. Circle 8

Step1: Calculate circumference

$C=2\pi r=2\times\pi\times9.3\approx58.4$ mm

Step2: Calculate area

$A=\pi r^2=\pi\times9.3^2\approx271.7$ mm²

2. Circle 10

Step1: Calculate circumference

$C=2\pi r=2\times\pi\times15.6\approx98.0$ m

Step2: Calculate area

$A=\pi r^2=\pi\times15.6^2\approx764.5$ m²

3. Circle 11

Step1: Find radius from diameter

$r=\frac{17}{2}=8.5$ yd

Step2: Calculate circumference

$C=2\pi r=2\times\pi\times8.5\approx53.4$ yd

Step3: Calculate area

$A=\pi r^2=\pi\times8.5^2\approx227.0$ yd²

4. Circle 12

Step1: Calculate circumference

$C=2\pi r=2\times\pi\times8.4\approx52.8$ m

Step2: Calculate area

$A=\pi r^2=\pi\times8.4^2\approx221.7$ m²

5. Problem 13

Step1: Solve for radius

$r=\frac{C}{2\pi}=\frac{80}{2\pi}\approx12.7$ km

6. Problem 14

Step1: Solve for radius

$r=\frac{C}{2\pi}=\frac{92}{2\pi}\approx14.6$ ft

7. Problem 15

Step1: Solve for radius

$r=\frac{C}{2\pi}=\frac{420}{2\pi}\approx66.8$ in

8. Problem 16

Step1: Solve for radius

$r=\frac{C}{2\pi}=\frac{700}{2\pi}\approx111.4$ km

9. Problem 17

Step1: Area of large circle

$A_{large}=\pi\times8^2=64\pi$ in²

Step2: Area of 3 small circles

$A_{small}=3\times\pi\times1^2=3\pi$ in²

Step3: Shaded area calculation

$A_{shaded}=64\pi-3\pi=61\pi\approx192$ in²

Answer:

1. $C\approx58.4$ mm, $A\approx271.7$ mm²
2. $C\approx98.0$ m, $A\approx764.5$ m²
3. $C\approx53.4$ yd, $A\approx227.0$ yd²
4. $C\approx52.8$ m, $A\approx221.7$ m²
5. $r\approx12.7$ km
6. $r\approx14.6$ ft
7. $r\approx66.8$ in
8. $r\approx111.4$ km
9. Shaded area $\approx192$ in²