Question

question 7 of 10 the circle shown below has a diameter of 18 centimeters. what is the approximate area of the shaded sector? a. 763 cm² b. 509 cm² c. 191 cm² d. 212 cm²

Explanation:

Step1: Find the radius

The diameter $d = 18$ cm, so the radius $r=\frac{d}{2}=\frac{18}{2}=9$ cm.

Step2: Calculate the area of the whole - circle

The formula for the area of a circle is $A=\pi r^{2}$. Substituting $r = 9$ cm, we get $A=\pi\times9^{2}=81\pi$ $cm^{2}$.

Step3: Find the area of the shaded sector

The central - angle of the shaded sector is $\theta = 270^{\circ}$. The formula for the area of a sector of a circle is $A_{sector}=\frac{\theta}{360^{\circ}}\times A_{circle}$. Substituting $\theta = 270^{\circ}$ and $A_{circle}=81\pi$ $cm^{2}$, we have $A_{sector}=\frac{270^{\circ}}{360^{\circ}}\times81\pi=\frac{3}{4}\times81\pi=\frac{243\pi}{4}\approx\frac{243\times3.14}{4}=\frac{763.02}{4}=190.755\approx191$ $cm^{2}$.

Answer:

C. $191$ $cm^{2}$