Diameter of the circular garden is 56m.There is a 4.5 m wide road around the garden .Find the area of the road
Answers
Given :
- Diameter of the circular garden = 56 m
- Width of a road around the garden = 4.5 m
To find :
- Area of the road
Concept :
To find the area of the road :-
- Firstly, we will calculate the radius of the circular garden.
- After getting the value of the radius of the circular garden substitute it's value in the formula of the area of circle, the resultant value will be the area of the circular garden.
- Now, add the width (4.5 m) of the road to the radius of the circular garden. The resultant value will be the radius of the circular garden including the road.
- To find the area of the road substract the area of the circular garden from the area of the circular garden including the road.
Formula to calculate raidus :-
- Radius = Diameter ÷ 2
Formula to calculate area of circle :-
- Area of circle = πr²
where,
- Take π = 22/7
- r = radius of the circle
Let's to do it →
Solution :
Radius of the circular garden :-
➪ Radius = Diameter ÷ 2
Substituting the given values, we get :-
➪ Radius = 56 ÷ 2
➪ Radius = 28
Therefore,
- Radius of the circular garden = 28 m
Area of the circular garden :-
➪ Area = πr²
Substituting the given values, we get :-
➪ Area = 22/7 × (28)²
➪ Area = 22/7 × 28 × 28
➪ Area = 22 × 4 × 28
➪ Area = 2464
Therefore,
- Area of the circular garden = 2464 m²
Radius of the circular garden including the road :-
➪ Radius = 28 + 4.5
➪ Radius = 32.5
Therefore,
- Radius of the circular garden including the road = 32.5 m
Area of the circular garden including the road :-
➪ Area = πr²
Substituting the given values, we get :-
➪ Area = 22/7 × (32.5)²
➪ Area = 22/7 × 32.5 × 32.5
➪ Area = 3,319.64
Therefore,
- Area of the circular garden including the road = 3,319.64 m²
Area of the road = Area of the circular garden including the road - Area of the road
➪ Area of the road = 3,319.64 - 2464
➪ Area of the road = 855.64
Therefore,
- Area of the road = 855.64 m²