Question

a circular flower bed is surrounded by a path 4 m wide . the diameter of a flower bed os 66 m . what is the area of path

Answer 1

 

Given that:-

Diameter of the flower bed(d) = 66 m

∴ Radius of the flower bed (r1) = 33 m

 

So, the area of the flower bed (A1) = πr12

 = 3.14 × 33 × 33

 = 3419.46 m2

Also the width of road is 4 m

∴ Radius of the flower bed with road (r2) = (33 + 4) m

 = 37 m

 

So the area of the flower bed with road (A2) = πr22

 = 3.14 × 37 × 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.

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