Answer:
Part one: r5 = 41.5 m , r6 = 42.75 m , r7 = 44 m , r8 = 45.25
Part two: Max ran 399.34 m in lane one
Part three: The distance in lanes 3 and 7 are 415.04 m and 446.46 m
Part four: Max ran in the three laps 1260.84 m around the track
Step-by-step explanation:
* lets explain how to solve the problem
- The school track has eight lanes
- Each lane is 1.25 meters wide
- The arc at each end of the track is 180° , that means the arc at each
end is a semi-circle
- The distance of the home straight for all lanes is 85 m
- The radius of the first lane is 36.5 m
∵ The width of each lane is 1.25
∴ The radius of the second lane = 36.5 + 1.25 = 37.75
- That means the radius of each lane increased by 1.25 then the
previous lane
∴ The radius of each lane = the radius of the previous lane + 1.25
# Part one:
∵ The radius of the 4 lane is 40.25
∴ The radius of the 5th lane = 40.25 + 1.25 = 41.5 m
∴ The radius of the 6th lane = 41.5 + 1.25 = 42.75 m
∴ The radius of the 7th lane = 42.75 + 1.25 = 44 m
∴ The radius of the 8th lane = 44 + 1.25 = 45.25 m
* r5 = 41.5 m , r6 = 42.75 m , r7 = 44 m , r8 = 45.25
- The length of each lane is the lengths of the 2 end arcs and 2
home straight distance
∵ The arc is a semi-circle
∵ The length of the semi-circle is πr
∴ The length of the 2 arcs is 2πr
∵ The length of the home straight distance is 85 m
∴ The length of each lane = 2πr + 2 × 85
∴ The length of each lane = 2πr + 170
# Part two:
- Max ran around lane one
∵ The radius of lane one = 36.5 m
∵ The distance of each lane = 2πr + 170
∴ The distance of lane one = 2π(36.5) + 170 = 399.34 m
* Max ran 399.34 m in lane one
# Part three:
- We will chose lanes 3 and 7
∵ The distance of each lane = 2πr + 170
∵ The radius of lane 3 = 39
∵ The radius of lane 7 is 44
∴ The distance of lane 3 = 2π(39) + 170 = 415.04 m
∴ The distance of lane 7 = 2π(44) + 170 = 446.46 m
* The distance in lanes 3 and 7 are 415.04 m and 446.46 m
# Part four:
- To find the total distance that Max ran in the 3 laps ad the answers
in part two and part three
∵ Max ran 399.34 m in lane one
∵ Max ran 415.04 m in lane three
∵ Max ran 446.46 m in lane seven
∴ The total distance of the 3 lanes = 399.34 + 415.04 + 446.46
∴ The total distance of the 3 lanes = 1260.84
* Max ran in the three laps 1260.84 m around the track
