inside perimeter of a running track show in the figure is 400 metre the length of each of the straight portion is 90 metre and the the ends of in semi circle if the track is 40 metre wild everywhere find the area of also find the length of outer boundary of the track
Answers
Solution:-
The inside perimeter of the track = 400 m
The total length of the two straight portions = 90 + 90 = 180 m
Therefore the length of the remaining portion = 400 - 180 = 220 m
Circumference of the two remaining semi-circular portions = πr + πr = 2πr
'r' is the radius.
⇒ 2πr = 220
2 × 22/7 × r = 220
44r = 220 × 7
r = (220 × 7)/44
r = 35 m
So, the radius of the circular portion of the outer running running track = 35 m + 40m = 75 m
Area of the track = Area of the two rectangles of dimensions 90 × 40 + The area of the circular rings.
= 2 × 90 × 40 + 22/7 × {(75)² - (35)²}
= 2520 + 22/7 ×(5625 - 1225)
= 2520 + (22 × 4400)/7
= 2520 + 96800/7
= 2520 + 13828.57
= 16348. 57 sq m
Length of the outer running track = 2 × 90 + 2 × 22/7 × 75
= 180 + 471.42
Length of the outer running track = 651.42m
Answer