the American hockey Federation organised the friendly hockey match between America and Australia on a circular ground the income of this match shall be donated to an or fungus a rectangular tough is sprayed on the ground as shown in figure
Answers
Given :-
Length of Rectangular turf = 80 m.
Breadth = 60 m .
To Find :-
1. the radius of the staduim is?
2. find the area of rectangular field
3. fine the perimeter of circular ground ( take circumference as 22/7)
4. find the area of circular ground.
5. find the area of shaded portion
Solution :-
from image we can see that,
→ ABCD = Rectangle .
→ AB = DC = 60 m .
→ CB = 80 m.
→ ∠DCB = 90° . (Each angle of a rectangle is equal to 90°.)
then, in Right ∆DCB, we have,
→ DC² + CB² = BD²
→ 60² + 80² = BD²
→ BD² = 3600 + 6400
→ BD² = 10000
→ BD = √(10000)
→ BD = 100 m
so,
→ Radius of the stadium = BD/2 = 100/2 = 50 m (Ans.1)
and,
→ Area of rectangular field = Length * Breadth = 60 * 80 = 4800 m². (Ans.2)
also,
→ The perimeter of circular ground = 2πr = 2 * (22/7) * 50 = (2200/7) = 314.28 m . (Ans.3)
and,
→ The area of circular ground = π(r)² = (22/7) * 50 * 50 = (55000/7) = 7857.14m² (Ans.4)
therefore,
→ The area of shaded region = The area of circular ground - Area of rectangular field = 7857.14 - 4800 = 3057.14m² (Ans.5)
