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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

3. Arcs and Chords

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Exercise 41 Page 740

Recall the formulas for the area of a square and the area of a circle.

F

Practice makes perfect

We are asked to write the ratio of the area of a circle to the area of a square. Let's take a look at the given diagram.

As we can see, the radius of the circle is 3r and the side length of the square is 2( 3r)= 6r. Using these values we can evaluate our ratio. Let's recall that the area of the circle is the product of pi and the squared radius, and the area of the square is the squared side length. A_c/A_s=π ( 3r)^2/( 6r)^2 Now we will simplify the ratio. We will start with distributing the powers to the terms in parentheses.

A_c/A_s=π (3r)^2/(6r)^2

(a b)^m=a^m b^m

A_c/A_s=π* 3^2r^2/6^2r^2

Calculate power

A_c/A_s=π* (9)r^2/36r^2

Multiply

A_c/A_s=9π r^2/36r^2

a/b=.a /r^2./.b /r^2.

A_c/A_s=9π/36

a/b=.a /9./.b /9.

A_c/A_s=π/4

The ratio is π4, which corresponds with answer F.

Subchapter links

Exercises p.736-740