In a village, there was no playground for children. If a child had to practice for any sports then
thechildhad to go to the city stadium which is 20 km from the village. But village has a circular unused
land and villagers decided to convert this unused land into a football ground, with athletic track around it,
so that children can practice their choice of sports in village itself. Villagers also planned six seating areas
with chairs (brown colour) and six seating area without chairs (grey colour) as shown in the figure.
Athletic track (light blue) is between the football ground (light green) and seating area. The distance
between the centre of the ground and the boundary of the stadium is 140 m, width of the athletic track is
30 m and AB is 20 m.
What is the length of the athletic track (inner boundary)?
Answers
Given : The distance between the centre of the ground and the boundary of the stadium is 140 m,
athletic track width is 30 m
AB = 20 cm
To Find : Area of Football ground
length of the athletic track (inner boundary)
the length of the athletic track (outer boundary)
area allocated for athletic track
area is allocated for six seating corners with chairs
total area used to develop this stadium
Solution:
The distance between the centre of the ground and the boundary of the stadium is 140 m,
athletic track width is 30 m
AB = 20 cm
Radius of Football ground = 140 - 30 - 20 = 90 m
Area of an circle = πr²
Area of Football ground = π (90)² = 8100π m²
length of the athletic track (inner boundary)
inner radius of athletic track = radius of Football ground
Perimeter = 2πr
= 2π (90)
= 180π m
the length of the athletic track (outer boundary)
= 2π (90 + 30)
= 240π m
area allocated for athletic track
= π(120)² - π(90)²
= π(210)(30)
=6300π m²
area is allocated for six seating corners with chairs
= π (140)² - 6 * ( √3/ 4) 140²
= π (140)² - 3 * ( √3/ 2) 140²
= 140² ( π - 3√3/ 2)
= 140² ( 2π - 3√3)/2
= 1,17,600 ( 2π - 3√3)/12
total area used to develop this stadium = π (140)²
= 19600π m²
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Step-by-step explanation:
1)8100pie
2)180pie
3)240pie
4)117600*(2pie-3√3/12)
5)19600pie