Question

activity 2. solve what is being asked then round your answers to the nearest tenths. use π = 3.1415 to approximate your answers. show your complete solution in your answer sheet. 1) if the diameter of a circle is 6 units, find the area of a sector with a sector - angle of 80°. 2) find the area of a sector with a radius of 10 cm and a central angle of 135°.

Explanation:

Step1: Find radius

For a circle with diameter $d = 6$ units, the radius $r=\frac{d}{2}=\frac{6}{2}=3$ units.

Step2: Use sector - area formula

The formula for the area of a sector of a circle is $A=\frac{\theta}{360}\times\pi r^{2}$, where $\theta$ is the central - angle in degrees and $r$ is the radius. Given $\theta = 80^{\circ}$ and $\pi=3.1415$, $r = 3$ units. Then $A=\frac{80}{360}\times3.1415\times3^{2}$.
First, calculate $3^{2}=9$. Then $\frac{80}{360}\times3.1415\times9=\frac{80\times3.1415\times9}{360}$.
$80\times3.1415\times9 = 80\times28.2735=2261.88$. And $\frac{2261.88}{360}\approx6.3$.

For the second part:

Step1: Identify values

Given $r = 10$ cm and $\theta = 135^{\circ}$, $\pi=3.1415$.

Step2: Apply sector - area formula

$A=\frac{\theta}{360}\times\pi r^{2}=\frac{135}{360}\times3.1415\times10^{2}$.
First, calculate $10^{2}=100$. Then $\frac{135}{360}\times3.1415\times100=\frac{135\times3.1415\times100}{360}$.
$135\times3.1415\times100 = 135\times314.15 = 42410.25$. And $\frac{42410.25}{360}\approx117.8$.

Answer:

1. $6.3$ square units
2. $117.8$ square cm