Question

The circumference of a circle is 11 cm and the angle of a sector of the circle is 60°. The area of the sector is $(use \pi=\frac{22}{7})$

• A. $$1\frac{29}{48}cm^2$$
• B. $$2\frac{29}{48}cm^2$$
• C. $$1\frac{27}{48}cm^2$$
• D. $2\frac{29}{48}cm^2$

Answer 1

Answer:

$$1\frac{29}{48}cm^2$$

Let the radius of the circle be r cm.

According to the question,

$2\pi{r} = 11$

$2\times{\frac{22}{7}}\times{r} = 11$

$r=\frac{11\times{7}}{2\times{22}}=\frac{7}{4}cm$

Area of the sector AOB $=\frac{\theta}{360^o}\times{\pi{r^2}}$

$=\frac{60^o}{360^o}\times{\frac{22}{7}}\times{\frac{7}{4}}\times{\frac{7}{4}}$

$=\frac{77}{48}=1\frac{29}{48}sqcm$