Question

question 7 of 10 true or false? to find the area of a sector, you multiply the area of the circle by the measure of the arc determined by the sector. a. true b. false

Explanation:

Step1: Recall sector - area formula

The area of a sector $A_{s}$ of a circle with radius $r$ and central - angle $\theta$ (in radians) is given by $A_{s}=\frac{1}{2}r^{2}\theta$. The area of the circle is $A = \pi r^{2}$. The formula for the area of a sector can also be written as $A_{s}=\frac{\theta}{2\pi}\times\pi r^{2}$, where $\frac{\theta}{2\pi}$ is the ratio of the central - angle of the sector to the full - circle angle ($2\pi$ radians). We multiply the area of the circle $\pi r^{2}$ by the ratio of the central - angle of the sector to the full - circle angle, not by the measure of the arc length. The arc length $l$ of a sector with radius $r$ and central - angle $\theta$ is $l = r\theta$. So the statement is false.

Answer:

B. False