mae has a oval racetrack. 2 curves, each is 1/2 of the circle and each on a radius of 21". 2 straight-aways connect the circle and are 46" long. what is the total distance around the circle?
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What is the distance around the track?
distance around the circle = 2π(21) = 42π or appr. 131.95 "
so around the track :
we would simply add 2(46) to that to get
223.95 "
To calculate the total distance around the oval racetrack, we need to find the circumference of each curve and add it to the length of the two straightaways.
First, let's find the circumference of the curves. The problem states that each curve is half a circle and is on a radius of 21". The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. Since each curve is half a circle, we can divide the circumference by 2.
Circumference of each curve = (2π * 21") / 2 = π * 21" = 21π"
Next, let's find the total length of the two straightaways, which is given as 46" each.
Total length of straightaways = 46" + 46" = 92"
Finally, we can find the total distance around the circle by summing the circumference of the curves and the length of the straightaways.
Total distance around the circle = 2 * (Circumference of each curve) + Total length of straightaways
= 2 * (21π") + 92"
= 42π" + 92"
Therefore, the total distance around the oval racetrack is 42π" + 92" (or approximately 92 + 42π inches).