Chapter Test
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The measure of an arc equals its corresponding central angle. Since the measure of the entire circle is 360^(∘), the measure of a major arc is the difference of 360^(∘) and the measure of the related minor arc. The area of a sector of a circle is the product of the area of the circle and the measure of the arc divided by 360^(∘).
142.4in^2
A sector of a circle is the region bounded by an arc of the circle and the two radii to the arc's endpoints.
Consider the figure below. Given that the radius of the circle is 8 inches, and the measure of ∠QSR is 105^(∘), we will find the area of the shaded sector in ⊙ S.
We can use the following formula to find the area of the shaded sector. Area of the shaded sector: mQTR/360* π r^2
We need first to calculate mQTR. Considering the fact that the measure of an arc equals its corresponding central angle, we can identify mQR. m∠QSR=105^(∘) ⇔ mQR= 105^(∘)
Recall that the measure of the entire circle is 360^(∘), and the measure of the major arc is the difference of 360^(∘) and the measure of the related minor arc. Therefore, we can calculate the measure of the major arc, mQTR, as follows. mQTR=360^(∘)- 105^(∘)= 255^(∘)
Now, we have all the information we need to use the formula to find the area of the shaded sector.
Calculate power
Commutative Property of Multiplication
a/c* b = a* b/c
a/b=.a /120./.b /120.
Use a calculator
Round to 1 decimal place(s)
The area of the shaded sector is about 142.4 square inches.