Question

A circular garden with radius 42 m is surrounded from
outside by a path of 3.5 m wide. Find the cost to pave the
stones on the path at the rate of Rs. 20 per m2.

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​

Answer 1

Internal Radius = 21 m, External Radius =20+3.5=24.5 m

Area of path = π(24.5)

2

−π(21)

2

⇒π[(24.5)

2

−(21)

2

]

=500.5

Cost of travelling =500.5×4=Rs.2002

Answer 2

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When path built then the new radius

become = 42+3.5 = 45.5m

Now

Cost = Area×Rate

Let the old radius be 'r' and new radius be 'R'

Area of the garden

π(R² - r²)

22/7(45.5² - 42²)

22/7 × (2070.25 - 1764)

22/7 × 306.25

9625m.

Now Cost = Rrea× Rate

Cost = 962.5×20

Cost = 19250