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QuestionBarret ran 8 laps on a circular track with a radius of 0.75 miles. How far did he run? Use C=2πrC = 2\pi r to find the distance.

Studdy Solution

STEP 1

Assumptions1. The track is circular in shape. The radius of the track is0.75 miles3. Barret completed8 laps

STEP 2

First, we need to find the circumference of the track, which is the distance around the circle. The formula for the circumference of a circle is given byCircumference=2πrCircumference =2\pi rwhere rr is the radius of the circle.

STEP 3

Now, plug in the given value for the radius to calculate the circumference.
Circumference=2π×0.75Circumference =2\pi \times0.75

STEP 4

Calculate the circumference of the track.
Circumference=2π×0.75=1.πCircumference =2\pi \times0.75 =1.\pi

STEP 5

Now that we have the circumference of the track, we can find the total distance Barret ran by multiplying the circumference by the number of laps.
Total distance=Circumference×Number of lapsTotal\, distance = Circumference \times Number\, of\, laps

STEP 6

Plug in the values for the circumference and the number of laps to calculate the total distance.
Total distance=1.5π×8Total\, distance =1.5\pi \times8

STEP 7

Calculate the total distance Barret ran.
Total distance=1.5π×=12πTotal\, distance =1.5\pi \times =12\piBarret ran 12π12\pi miles.

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