Question

question 5 of 10 what is the approximate area of the shaded sector in the circle shown below? a 2.83 cm² b. 5.09 cm² c. 5.65 cm² d. 20.36 cm²

Explanation:

Step1: Find the radius

The diameter is 3.8 cm, so the radius $r=\frac{3.8}{2}=1.9$ cm.

Step2: Use the 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 of the sector and $r$ is the radius of the circle. Here, $\theta = 150^{\circ}$ and $r = 1.9$ cm.
Substitute the values into the formula: $A=\frac{150}{360}\times\pi\times(1.9)^{2}$.
First, calculate $(1.9)^{2}=3.61$.
Then, $\frac{150}{360}=\frac{5}{12}$.
So, $A=\frac{5}{12}\times\pi\times3.61$.
$A=\frac{5\times3.61\pi}{12}=\frac{18.05\pi}{12}$.
Taking $\pi\approx3.14$, we have $A=\frac{18.05\times3.14}{12}=\frac{56.677}{12}\approx4.72$. But if we calculate more precisely:
$A=\frac{150}{360}\times3.14\times(1.9)^{2}=\frac{5}{12}\times3.14\times3.61 = 5.09$ (approx).

Answer:

B. $5.09$ cm²