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


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


Solve for r using 


Divide both sides of the equation by 3.14


Simplify.


Take the square root of both sides of the equation.


Simplify.

or 

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

Substitute 10 for r in the circumference equation. Use  again.



Simplify.


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