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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Circles and Circumference

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Exercise 47 Page 722

Practice makes perfect

a We are asked to determine how much greater is the circumference of the outermost circle than the circumference of the center circle. To do this we will evaluate the difference of the circumferences using the formula for the circumference of a circle.

C_O-C_C=2π r_O-2π r_C The radius of the outermost circle is 30 miles and the radius of the center circle is 5. Let's substitute these radii into the equation.

2π r_O-2π r_C

r_C= 5, r_O= 30

2π* 30-2π* 5

Factor out 2π

2π(30-5)

Subtract term

2π (25)

Multiply

50π

Use a calculator

157.0796...

The circumference of the outermost circle is approximately 157.1 miles greater than the circumference of the center circle.

b Now let's analyze how the circumference changes when radius increases.

Change in r	r	C=2π r	Change in C
	5	10π
+5	10	20π	+10π
+5	15	30π	+10π
+5	20	40π	+10π
+5	25	50π	+10π
+5	30	60π	+10π

As we can see — as r increases by 5, the circumference C increases by 10π, which is approximately 31.4 miles.

Subchapter links

Exercises p.719-723