Question

question 3 of 10 what is the approximate area of the shaded sector in the circle shown below? a. 34.6 in² b. 9.36 in² c. 17.3 in² d. 4.68 in²

Explanation:

Step1: Recall area - of - sector 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.

Step2: Identify given values

We are given that $r = 3.7$ inches and $\theta=145^{\circ}$.

Step3: Substitute values into formula

$A=\frac{145}{360}\times\pi\times(3.7)^{2}$.

Step4: Calculate $(3.7)^{2}$

$(3.7)^{2}=3.7\times3.7 = 13.69$.

Step5: Calculate the fraction times $\pi$ times $(3.7)^{2}$

$A=\frac{145}{360}\times\pi\times13.69$.
$\frac{145}{360}\approx0.4028$, and $0.4028\times\pi\times13.69$.
Taking $\pi\approx3.14$, we have $0.4028\times3.14\times13.69$.
$0.4028\times3.14 = 1.2658$, and $1.2658\times13.69\approx17.3$. So the area of the sector is approximately $17.3\text{ in}^2$.

Answer:

C. $17.3\text{ in}^2$