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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. Secants, Tangents, and Angle Measures

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Exercise 45 Page 767

The circumference of a circle is twice the radius multiplied by π. Notice that each shaded region represents one-quarter of the area of the circle.

B

Practice makes perfect

We are given the following circle whose circumference is 16π units.

To find the radius of the circle, we use the fact that its circumference is obtained by multiplying two twice the radius with π.

C = 2π r ⇒ 16π = 2π r From the equation above, we can get that r=8 units. Therefore, the area of the entire circle is A=8^2π, or 64π units^2. Finally, notice that each shaded area represents one-quarter of the circle.

The total area of the shaded regions is given by the expression below. Shaded Area = 1/4A + 1/4A Let's substitute the area of the circle into the equation above to find the area of the shaded regions.

Shaded Area = 1/4A + 1/4A

A= 64π

Shaded Area = 1/4( 64π) + 1/4( 64π)

▼

Simplify

Multiply

Shaded Area = 16π + 16π

Add terms

Shaded Area = 32π

In conclusion, the total area of the shaded regions is 32π units^2, which tells us that the correct choice is option B.

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Exercises p.763-767