Question

4.4 circumference and area of a circle
find the circumference and area of each circle. use 3.14 for π and round your answer to the nearest hundredth. (two decimal places.)
a.
12 in
c = in.
a = in²
b.
22cm
c = cm
a = cm²
c.
12 cm
c = cm
a = cm²

Explanation:

Step1: Recall circle - formulas

The formula for the circumference of a circle is $C = 2\pi r=\pi d$ (where $r$ is the radius and $d$ is the diameter), and the formula for the area of a circle is $A=\pi r^{2}$.

Step2: Solve for circle a

The diameter $d = 12$ in. So the radius $r=\frac{d}{2}=6$ in.
Circumference: $C=\pi d=3.14\times12 = 37.68$ in.
Area: $A=\pi r^{2}=3.14\times6^{2}=3.14\times36 = 113.04$ in².

Step3: Solve for circle b

The diameter $d = 22$ cm. So the radius $r = 11$ cm.
Circumference: $C=\pi d=3.14\times22=69.08$ cm.
Area: $A=\pi r^{2}=3.14\times11^{2}=3.14\times121 = 379.94$ cm².

Step4: Solve for circle c

The radius $r = 12$ cm.
Circumference: $C = 2\pi r=2\times3.14\times12=75.36$ cm.
Area: $A=\pi r^{2}=3.14\times12^{2}=3.14\times144 = 452.16$ cm².

Answer:

a. $C = 37.68$ in, $A = 113.04$ in²
b. $C = 69.08$ cm, $A = 379.94$ cm²
c. $C = 75.36$ cm, $A = 452.16$ cm²