SOLUTION: if a circular track has an area of 314 ft squared, how many feet is twice around the track?

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Question 858811: if a circular track has an area of 314 ft squared, how many feet is twice around the track?
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,

Your Problem:
if a circular track has an area of 314 ft squared, how many feet is twice around the track?

Solution:
The track is circular so the formula for its area is
A=pi%2Ar%5E2

We want to know the distance twice around the track. The distance once around a circular track is the 
circumference. The formula for the circumference is 
C = 2*pi*r}}}

We need to convert the area information into circumference information. We will use the area equation 
to find the radius of the track, then use this radius to find the circumference.

We are given that the area is 314 square feet, so A = 314. Our area equation becomes
314=pi%2Ar%5E2

Solve for r using pi=3.14
314=3.14%2Ar%5E2

Divide both sides of the equation by 3.14
314%2F3.14=%283.14%2Ar%5E2%29%2F3.14

Simplify.
100=r%5E2

Take the square root of both sides of the equation.
sqrt%28100%29=sqrt%28r%5E2%29

Simplify.
10=r
or r=10

In the context of this problem, r = 10 means that radius is 10 feet.

Substitute 10 for r in the circumference equation. Use pi=3.14 again.
C=2%2Api%2Ar
C=%282%29%283.14%29%2810%29

Simplify.
C=62.8

In the context of this problem, C=62.8 means that the circumference is 62.8 feet. We want to know the 
distance twice around the track so we double this amount: 62.8*2 = 125.6

The distance twice around the track is 125.6 feet.

Hope this helps! Feel free to email me if you have questions about the solution.

Mrs Figgy
math.in.the.vortex@gmail.com