The inside perimeter of a running track is 400m.The length of each of the straight portion is 90m and the end are semicircles. If the track is everywhere14m wide, find the area of the track. Also, find the length of outer running track.
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Solution:-
The inside perimeter of the track = 400 m
Total length of the two portion = 2*90 = 180 m
Therefore, the length of the remaining portion = 400 - 180 = 220 m
Circumference of the remaining semi-circular portions = πr + πr = 2πr
2πr = 220
2*22/7r = 220
r = 1540/44
r = 35 m
therefore, the radius of the circular portion of the outer running track
= 35 + 14 = 49 m
Area of the track = area of the two rectangles + area of the circular rings
= 2 × 90 × 14 + 22/7 × {(49)² - (35)²}
= 2520 + 22/7(2401 - 1225)
= 2520 + (22*1176)/7
= 2520 + (22*168)
= 2520 + 3696
Area = 6216 sq m
Now, the length of the outer running track = (2 × 90) + (2 × 22/7 × 49)
= 180 + 308
Length of the outer running track = 488 m
Answer.
The inside perimeter of the track = 400 m
Total length of the two portion = 2*90 = 180 m
Therefore, the length of the remaining portion = 400 - 180 = 220 m
Circumference of the remaining semi-circular portions = πr + πr = 2πr
2πr = 220
2*22/7r = 220
r = 1540/44
r = 35 m
therefore, the radius of the circular portion of the outer running track
= 35 + 14 = 49 m
Area of the track = area of the two rectangles + area of the circular rings
= 2 × 90 × 14 + 22/7 × {(49)² - (35)²}
= 2520 + 22/7(2401 - 1225)
= 2520 + (22*1176)/7
= 2520 + (22*168)
= 2520 + 3696
Area = 6216 sq m
Now, the length of the outer running track = (2 × 90) + (2 × 22/7 × 49)
= 180 + 308
Length of the outer running track = 488 m
Answer.
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