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A park is of the shape of a circle of diameter $7 m$ . It is surrounded by a path of width of $0 ⋅ 7 m$ . Find the expenditure of cementing the path, if its cost is ₹ 110 per sq. m.

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₹ 1000.25

₹ 1863.4

None of these

₹ 564.55

answer is A.

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Detailed Solution

Given that, Diameter of the circular park is 7 m. and width of the path around the park is 0.7 m.
We know that, Area of circle with radius r units is equal to

π r 2

.
Dividing 7 by 2 to determine the radius of the circular park.

r = 72

⇒

3.5
Let A

1

be the area of the circular park.
Substitute 3.5 for r into

π r 2

to determine the area of the circular park.

A 1 = π 3.5 2

⇒ 227 × 12.25

⇒ 22 × 175

⇒

38.5
Adding 0.7 to 3.5 to determine the radius of the outer circle.

3.5 + 0.7 = 4.2

Let A

2

be the area of the circular park. Substitute 4.2 for r into

π r 2

to determine the area of the outer circle.

A 2 = π 4.2 2

⇒ 227 × 17.64

⇒ 22 × 2.52

⇒

55.44
Let A

2

be the area of the circular path. Subtract the value of

A 1

from

A 2

to determine the area of the circular path.

A p = A 2 − A 1

⇒ 55.44 − 38.5

⇒

16.94
The cost of cementing one square meter is ₹110.
Multiply 16.94 by 110 to determine the cost of cementing the circular path around the park.

16.94 × 110 = 1863.4

Therefore, the cost of cementing the circular path around the park is ₹1863.4.
Hence the correct option is 1.

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