Math, asked by Hemadeep, 1 month ago

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

Answered by amitnrw
27

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

Learn More:

What is the area of the shaded portion of the circle? (5π – 11.6) ft2 ...

brainly.in/question/10536310

find the area of the shaded region in the following figure - Brainly.in

brainly.in/question/8104770

Abcd is a square with side 2√2 cm and inscribed in a circle find the ...

brainly.in/question/8916178

Attachments:
Answered by krishnavenimahendran
6

Step-by-step explanation:

1)8100pie

2)180pie

3)240pie

4)117600*(2pie-3√3/12)

5)19600pie

Attachments:
Similar questions