the distance between the two inner parallel line segments is 60 and they are each 106m long. if the track is 10m wide, find,
1) the distance around the track along its inner edge and
2) the area of the track
Answers
Find the radius of the inner track:
Radius = Diameter ÷ 2
Radius = 60 ÷ 2 = 30 m
Find the distance of the inner track:
Distance = 2πr + Length + Length
Distance = 2π(30) + 106 + 106 = 400.57 m
Find the area of the inner track:
Area = πr² + (Length x Breadth)
Area = π(30)² + (106 x 60)
Area = 9188.57 m²
Find the area of the whole track:
Area = πr² + (Length x Breadth)
Radius =30 + 10 = 40 m
Width =60 + 10 + 10 = 80 m
Area = π(40)² + (106 x 80)
Area = 13508.57 m²
Find the area of the track:
Area = 13508.57 - 9188.57 = 4320 m²
Answer: (1)400.57 m (2) 4320 m²
Width of track = 10 m
Distance between two parallel lines = 60 m
Length of parallel tracks = 106 m
DE = CF = 60 m
Radius of inner semicircle, r = OD = O'C
= 60/2 m = 30 m
Radius of outer semicircle, R = OA = O'B
= 30 + 10 m = 40 m
Also, AB = CD = EF = GH = 106 m
Distance around the track along its inner edge = CD + EF + 2 × (Circumference of inner semicircle)
= 106 + 106 + (2 × πr) m = 212 + (2 × 22/7 × 30) m
= 212 + 1320/7 m = 2804/7 m
Area of the track = Area of ABCD + Area EFGH + 2 × (area of outer semicircle) - 2 × (area of inner semicircle)
= (AB × CD) + (EF × GH) + 2 × (πr2/2) - 2 × (πR2/2) m2
= (106 × 10) + (106 × 10) + 2 × π/2 (r2 -R2) m2
= 2120 + 22/7 × 70 × 10 m2
= 4320 m2