Question

practice

figure	circumference (perimeter)	area
2. <br><img src=unknown alt=circle with radius 5 m width=100>
3. <br><img src=unknown alt=quarter - circle with radius 5 m width=100>
4. <br><img src=unknown alt=semicircle with diameter 13 cm width=100>

Explanation:

Step1: Recall circle - related formulas

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

1.

• Circumference (Perimeter): Given $d = 16$ cm, $r=\frac{d}{2}=8$ cm. Using the formula $C=\pi d$, we have $C = 16\pi\approx16\times3.14 = 50.24$ cm.
• Area: Using the formula $A=\pi r^{2}$, with $r = 8$ cm, $A=\pi\times8^{2}=64\pi\approx64\times3.14 = 200.96$ $cm^{2}$.

2.

• Circumference (Perimeter): Given $r = 5$ m. Using the formula $C = 2\pi r$, we have $C=2\pi\times5 = 10\pi\approx10\times3.14=31.4$ m.
• Area: Using the formula $A=\pi r^{2}$, with $r = 5$ m, $A=\pi\times5^{2}=25\pi\approx25\times3.14 = 78.5$ $m^{2}$.

3.

• Circumference (Perimeter): The curved part of the perimeter of a quarter - circle is $\frac{1}{4}$ of the circumference of the full - circle. Given $r = 5$ m, the circumference of the full - circle is $C = 2\pi r=10\pi$ m. The curved part of the quarter - circle is $\frac{1}{4}\times10\pi=\frac{5\pi}{2}$ m. The total perimeter $P=\frac{5\pi}{2}+5 + 5=\frac{5\pi}{2}+10\approx\frac{5\times3.14}{2}+10=7.85 + 10=17.85$ m.
• Area: The area of a quarter - circle is $\frac{1}{4}$ of the area of the full - circle. With $r = 5$ m, the area of the full - circle is $A=\pi r^{2}=25\pi$ $m^{2}$. So the area of the quarter - circle is $\frac{1}{4}\times25\pi=\frac{25\pi}{4}\approx\frac{25\times3.14}{4}=19.625$ $m^{2}$.

4.

• Circumference (Perimeter): Given $d = 13$ cm, $r=\frac{13}{2}$ cm. The curved part of the semi - circle is $\frac{1}{2}\pi d=\frac{13\pi}{2}$ cm. The total perimeter $P=\frac{13\pi}{2}+13\approx\frac{13\times3.14}{2}+13=20.41+13 = 33.41$ cm.
• Area: The area of a semi - circle is $\frac{1}{2}\pi r^{2}$. Since $r=\frac{13}{2}$ cm, $A=\frac{1}{2}\pi\times(\frac{13}{2})^{2}=\frac{169\pi}{8}\approx\frac{169\times3.14}{8}=66.3325$ $cm^{2}$.

Answer:

Figure	Circumference (Perimeter)	Area
2	$31.4$ m	$78.5$ $m^{2}$
3	$17.85$ m	$19.625$ $m^{2}$
4	$33.41$ cm	$66.3325$ $cm^{2}$