Question

henry constructed circle a with a radius of 10 units. he then created a sector as shown in the figure below. which of the following expressions would help him find the area of the shaded sector?

Explanation:

Step1: Recall area - of - circle formula

The area of a full - circle is given by $A = \pi r^{2}$, where $r$ is the radius of the circle. Here, $r = 10$ units, so the area of circle $A$ is $A=\pi\times(10)^{2}=100\pi$ square units.

Step2: Find the fraction of the circle the sector represents

The central angle of the full - circle is $360^{\circ}$, and the central angle of the given sector is $120^{\circ}$. The fraction of the circle that the sector represents is $\frac{120}{360}=\frac{1}{3}$.

Step3: Calculate the area of the sector

The area of the sector is the fraction of the circle times the area of the full - circle. So the area of the sector $S=\frac{120}{360}\times\pi r^{2}=\frac{1}{3}\times100\pi=\frac{100\pi}{3}$ square units.

Answer:

The expression to find the area of the shaded sector is $\frac{120}{360}\times\pi\times(10)^{2}$ or $\frac{100\pi}{3}$.