Question

find the circumference and area of these circles
circle
circumference
area

Explanation:

Step1: Recall circle - related formulas

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

Step2: Calculate for the first circle with $d = 12.5$ cm

$r=\frac{d}{2}=6.25$ cm. $C=\pi d = 12.5\pi\approx12.5\times3.14 = 39.25$ cm, $A=\pi r^{2}=\pi\times(6.25)^{2}\approx3.14\times39.0625 = 122.65625$ $cm^{2}$.

Step3: Calculate for the second circle with $r = 1.5$ cm

$C = 2\pi r=2\times\pi\times1.5 = 3\pi\approx3\times3.14 = 9.42$ cm, $A=\pi r^{2}=\pi\times(1.5)^{2}\approx3.14\times2.25 = 7.065$ $cm^{2}$.

Step4: Calculate for the third circle with $d = 4.5$ cm

$r=\frac{d}{2}=2.25$ cm. $C=\pi d = 4.5\pi\approx4.5\times3.14 = 14.13$ cm, $A=\pi r^{2}=\pi\times(2.25)^{2}\approx3.14\times5.0625 = 15.89625$ $cm^{2}$.

Step5: Calculate for the fourth circle with $r = 6.5$ cm

$C = 2\pi r=2\times\pi\times6.5 = 13\pi\approx13\times3.14 = 40.82$ cm, $A=\pi r^{2}=\pi\times(6.5)^{2}\approx3.14\times42.25 = 132.665$ $cm^{2}$.

Step6: Calculate for the fifth circle with $d = 3$ cm

$r=\frac{d}{2}=1.5$ cm. $C=\pi d = 3\pi\approx3\times3.14 = 9.42$ cm, $A=\pi r^{2}=\pi\times(1.5)^{2}\approx3.14\times2.25 = 7.065$ $cm^{2}$.

Step7: Calculate for the sixth circle with $r = 2$ cm

$C = 2\pi r=2\times\pi\times2 = 4\pi\approx4\times3.14 = 12.56$ cm, $A=\pi r^{2}=\pi\times(2)^{2}\approx3.14\times4 = 12.56$ $cm^{2}$.

Step8: Calculate for the seventh circle with $d = 7$ cm

$r=\frac{d}{2}=3.5$ cm. $C=\pi d = 7\pi\approx7\times3.14 = 21.98$ cm, $A=\pi r^{2}=\pi\times(3.5)^{2}\approx3.14\times12.25 = 38.465$ $cm^{2}$.

Step9: Calculate for the eighth circle with $r = 3$ cm

$C = 2\pi r=2\times\pi\times3 = 6\pi\approx6\times3.14 = 18.84$ cm, $A=\pi r^{2}=\pi\times(3)^{2}\approx3.14\times9 = 28.26$ $cm^{2}$.

Answer:

Circle	Circumference (cm)	Area ($cm^{2}$)
2	9.42	7.065
3	14.13	15.89625
4	40.82	132.665
5	9.42	7.065
6	12.56	12.56
7	21.98	38.465
8	18.84	28.26