Question

A circular flower bed is surrounded by a path 4 wide. the diameter of the flower bed is 66 m, what is the area of this path? (π = 3.14)

Answer 1

Diameter of the flower bed(d) = 66 m

∴ Radius of the flower bed (r 1) = 33 m

 

So, the area of the flower bed (A1) = πr 1 2

= 3.14 x 33 x 33

= 3419.46 m2

Also the width of road is 4 m

∴ Radius of the flower bed with road (r 2) = (33 + 4) m

= 37 m

 

So the area of the flower bed with road (A2) = πr2 2

= 3.14 x 37 x 37

= 4298.66 m2

 

Hence the area of the road = (Area of the flower bed with road) – (Area of flower bed)

= A2 – A1

= 4298.66 - 3419.46 m2

= 879.20 m2

Answer 2

Given:-

Width of the path = 4 m

Diameter of the flower bed = 66 m

To find:-

The area of the path.

Solution:-

Diameter of the flower bed is 66 m.

So, Radius of the flower bed =diameter/2

= (66/2)m

= 33m.

Now, Area of flower bed =  π r²

⟹ Area = 3.14 × (33)²

⟹Area = 3.14 × 1089.

⟹Area = 3419.49 m²

Now, Diameter of large circle

= Width of path + diameter of flower bed.

= ( 66 + 4)m

= 70m

So, Radius of large circle

= (diameter/ 2)

= (70/2)m

= 35 m.

Now, Area of large circle =  π r²

➟Area = 3.14 × (35)²

➟Area = 3.14 × 1225.

➟Area = 3846.5

So, now Area of path

= Area of large circle - Area of flower bed

= 3846.5 - 3419.49

= 427.01 m² (ans)

Therefore, the area of the path is 427.01 m².

_________________________________

${\boxed{\huge{\underline{\mathbb{Your\:Answer}}}}}$