Question

complete the chart. 20

figure	circumference (perimeter)	area
2. <br><img src=circle with radius 3.7 m />
3. <br><img src=quarter - circle with radius 4.4 m />
4. <br><img src=semicircle with diameter 22 km />

Explanation:

Step1: Recall circle formulas

The circumference of a full - circle is $C = 2\pi r=\pi d$ and the area of a full - circle is $A=\pi r^{2}$, where $r$ is the radius and $d$ is the diameter. For a semi - circle, the curved part length is $\frac{1}{2}C$ and the perimeter includes the diameter. For a quarter - circle, the curved part length is $\frac{1}{4}C$ and for a sixth - circle, the curved part length is $\frac{1}{6}C$.

Step2: Solve for circle 1

Given $d = 14$ cm, so $r=7$ cm.
Circumference $C=\pi d=\pi\times14\approx 43.98$ cm.
Area $A = \pi r^{2}=\pi\times7^{2}=49\pi\approx153.94$ $cm^{2}$.

Step3: Solve for circle 2

Given $r = 3.7$ m.
Circumference $C = 2\pi r=2\pi\times3.7\approx23.24$ m.
Area $A=\pi r^{2}=\pi\times(3.7)^{2}\approx42.98$ $m^{2}$.

Step4: Solve for the quarter - circle (circle 3)

Given $r = 4.4$ m.
The curved part length of the quarter - circle is $\frac{1}{4}\times2\pi r=\frac{1}{4}\times2\pi\times4.4=\frac{4.4\pi}{2}\approx6.91$ m.
The perimeter $P=\frac{1}{4}\times2\pi r + 2r=6.91+2\times4.4=6.91 + 8.8 = 15.71$ m.
The area $A=\frac{1}{4}\pi r^{2}=\frac{1}{4}\pi\times(4.4)^{2}\approx15.20$ $m^{2}$.

Step5: Solve for the semi - circle (circle 4)

Given $d = 22$ km, so $r = 11$ km.
The curved part length of the semi - circle is $\frac{1}{2}\times\pi d=\frac{1}{2}\times\pi\times22 = 11\pi\approx34.56$ km.
The perimeter $P=\frac{1}{2}\times\pi d+d=11\pi + 22\approx34.56+22=56.56$ km.
The area $A=\frac{1}{2}\pi r^{2}=\frac{1}{2}\pi\times11^{2}=\frac{121\pi}{2}\approx189.97$ $km^{2}$.

Answer:

Figure	Circumference (Perimeter)	Area
2.	$\approx23.24$ m	$\approx42.98$ $m^{2}$
3.	$\approx15.71$ m	$\approx15.20$ $m^{2}$
4.	$\approx56.56$ km	$\approx189.97$ $km^{2}$