Exercise 3 Page 868

The length of an arc of a circle is the product of the circumference of the circle and the measure of the arc divided by 360.

Practice makes perfect

We know that a Ferris wheel has a diameter of 68 feet and we want to find the distance a person on the Ferris wheel will travel while the wheel rotates 12^(∘).

As we can see, a person on the wheel moves in an arc when the wheel is rotating. Also, the measure of our arc is 12^(∘). Let's review how we can calculate the arc length when given its measure.

arc length/circumference = arc measure/360^(∘) We already know that the arc measure is 12^(∘). Now we need to find the circumference of our circle. When we know the circumference, we will be able to calculate the arc length. Let's recall the formula for the circumference C of a circle. Remember, the diameter d is twice the radius r. C= 2π r ⇔ C = π d Let's substitute 68 for d in this formula and simplify to obtain the circumference.

C = π d

Substitute

d= 68

C = π( 68)

Multiply

C = 213.628300...

RoundDec

Round to 2 decimal place(s)

C ≈ 213.63

The circumference of the Ferris wheel is approximately 213.63. Now, we can substitute the values of the circumference and arc measure into the appropriate formula and calculate the arc length.

arc length/C = arc measure/360

SubstituteII

C= 213.63, arc measure= 12

arc length/213.63 = 12/360

ReduceFrac

a/b=.a /12./.b /12.

arc length/213.63 = 1/30

MultEqn

LHS * 213.63=RHS* 213.63

arc length = 213.63/30

CalcQuot

Calculate quotient