Question

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

Answer 1

Step-by-step explanation:

Given:

• Width of path is 4 m.
• Diameter of flower bed is 66 m.

To Find:

• What is the area of path ?

Solution: Here diameter of flower bed is 66 m. Therefore,

➟ Radius of flower bed = Diameter/2

➟ Radius = 66/2 = 33 m

[ In larger circle ]

• Radius of larger circle = Radius of flower bed + Width of park

➟ Radius = 33 + 4/100

➟ 33 + 0.04 = 33.04 m

As we know that

★ Area of Circle = πr² ★

$\implies{\rm }$ π(33.04)²

$\implies{\rm }$ 1091.64π m²

[ In smaller circle ]

• Radius is 33 m

$\implies{\rm }$ π(33)³

$\implies{\rm }$ 1089π m²

Now, Area of path = Area (larger circle – smaller flower bed)

➬ Area = (1091.64π) – (1089π)

➬ Area = (1091.64 – 1089)π

➬ Area = 2.64(3.14)

➬ Area = 8.28 m²

Hence area of path is 8.28 m²

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{ This question is not correct according to the book Width of flower park is 4 metre }

Now, taking width as 4 m.

[ In larger circle ]

• Radius of larger circle = Radius of flower bed + Width of park

➟ Radius = 33 + 4 = 37 m

$\implies{\rm }$ Area = π(37)²

$\implies{\rm }$ 1369π m²

[ In smaller circle ]

$\implies{\rm }$ Area = π(33)²

$\implies{\rm }$ 1089π m²

Now, Area of path = Area (larger circle – smaller flower bed)

➬ Area = 1369π – 1089π

➬ Area = (1369 – 1089)π

➬ Area = 280(3.14)

➬ Area = 879.2 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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