A sports field has a 90 m by 70 m football field with a semi-circular area at each end a truck runs around the perimeter of the sports field area of the sports field the length of one loop of the track used pi equals to 22 / 7
Answers
Answer:
Step-by-step explanation:
I am assuming here that semi circle is at each shorter end
area of track - area1.jpg
total length of track - length_track.jpg
The length of one loop of the track is 502.85 m.
Given: The length and breadth of a football field are 90 m and 70 m. There are semi-circular tracks at each end of the track.
To Find: The length of one loop of the track.
Solution:
- We are said that there is a semi-circular track at each end of the football field. So, there are four ends of a track, 2 along the length and 2 along the breadth.
- To find the length of a semi-circular track, we need to find the perimeter ( or length of circumference ) of a semi-circular track, which is given by the formula,
Perimeter = πR ......(1)
where R = radius of the semi-circle.
Coming to the numerical, we are given the length and breadth of the football field.
The length of the football field = is 90 m
So, the radius of the semi-circle along the length = 90/2 m
= 45 m
So, the perimeter of the semi-circle along the length = π × 45 m
Since there are two lengths in a rectangle, so perimeter = 2π×45 m
= 90π m
The breadth of the football field = is 70 m
So, the radius of the semi-circle along the breadth = 70/2 m
= 35 m
So, the perimeter of the semi-circle along the length = π × 35 m
Since there are two lengths in a rectangle, so perimeter = 2π×35 m
= 70π m
So, total length of the loop = ( 90π + 70π ) m
= 160 × ( 22/7 ) m
= 502.85 m
Hence, the length of one loop of the track is 502.85 m.
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