Question

Chapter 11
A circular flower bed is surrounded by a path 4 m
wide. The diameter of the flower bed is 66 m. What
is the area of this path ? (n = 3.14)​

Answer 1

Answer:

Diameter of the circular flower bed = 66 m

So, radius of circular flower bed = 66/2 = 33 m

Radius of circular flower bed with 4 m wide path (R) = 33 + 4 = 37

According to the question,

Area of path = Area of bigger circle – Area of smaller circle

= πR2 – πr2

= π(R2 – r2)

= π(372 – 332)

= π(37 + 33)*(37 - 33)

[(a2 – b2) = (a - b)*(a + b)]

= 3.14 * 70 * 4

= 879.20 m2

Therefore, the area of the path is 879.20 m2

Hope it helps you!

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@PrettyNancy

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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