#1) 163.81 m
#2) About 9.8 laps.
#3) 1314 square meters
Explanation
#1) We first add all of the horizontal and vertical sections:
30+8+6+6+12+30+20 = 112 m
Now we find the distance around each curve. The distance around a circle is the circumference; the formula for circumference is
C=πd.
We will use 3.14 for π for each curve:
Curve 5: The radius is 3, so the diameter is 2*3 = 6. This is 1/4 of a curve, so we multiply the circumference by 1/4:
1/4(3.14)(6) = 4.71
Curve 4: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 3: This is 1/2 of a curve, so we will multiply the circumference by 1/2. The radius is 2.25, so the diameter is 2*2.25 = 4.5:
1/2(3.14)(4.5) = 7.065
Curve 2: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 1: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 9: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 8: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 7: This is another 1/2 curve with a radius of 2.25, so the distance around is 7.065, just as curve 3.
Curve 6: This is 1/2 of a curve with a radius of 3, so the distance around is 1/2(3.14)(2*3) = 9.42
The total distance around the curved parts is:
4.71+4.71+7.065+4.71+4.71+4.71+4.71+7.065+9.42 = 51.81
Together this gives us 112+51.81 = 163.81.
#2) To find the number of laps it takes to go 1609 meters, divide:
1609/163.81 = 9.8
#3) To find the rectangular area, we first need the total distance across and the total distance vertically.
Horizontally, we have a radius of 3, a horizontal distance of 30, and another radius of 3:
3+30+3 = 36
(looking at the right hand side)
Vertically, we have a radius of 3, vertical distance of 8, radius of 3, radius of 2.25, radius of 2.25, radius of 3, vertical distance of 12, and radius of 3:
3+8+3+2.25+2.25+3+12+3 = 36.5
The area is then 36(36.5) = 1314 m²
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