Q. 45.0( 2 Votes )

The circumference of a circular park is 314 m. A 20 m. wide concrete track runsround it. CalculateÂ the cost of laying turf in the park at Rs1.25 persq.m. and the cost of concrete track at Rs 1.25 perÂ sq. m.

Answer :

Let the radius of park including track (i.e. outside circle) be 'r _{ 1 } ' and radius of park without including (i.e. inner circle) track be 'r _{ 2 } '.

Given,

Circumference of Park = 314 m

we know that,

circumference of a circle = 2πr

where 'r' is the radius of the circle.

⇒ 2πr _{ 1 } = 314

⇒ 2 × 3.14 × r _{ 1 } = 314

⇒ 2r _{ 1 } = 100 m

⇒ r _{ 1 } = 50 m

Also, area of circle = πr ^{ 2 } , where 'r' is the radius of circle.

⇒ area of outer circle = πr _{ 1 } ^{ 2 } = 3.14 × (50) ^{ 2 } = 7850 m ^{ 2 } [1]

Also,

Radius of park excluding the track, r _{ 2 } = r _{ 1 } - width of track = 50 - 20 = 30 m

⇒ area of inner circle = πr _{ 2 } ^{ 2 } = 3.14 × (30) ^{ 2 } = 2826 m ^{ 2 }

Now,

Area of laying turf in the park = area of inner circle = 2826 m ^{ 2 }

Cost of laying 1 m ^{ 2 } = 1.25 Rs

⇒ Cost of laying 2826 m ^{ 2 } = 2826(1.25) = 3532.5 Rs

Also,

Area of track = Area of outer circle - Area of inner circle

⇒ Area of track = 7850 - 2826 = 5024 m ^{ 2 }

Cost of concrete 1 m ^{ 2 } of track = 1.25 Rs

Cost of concrete 5024 m ^{ 2 } of track = 5024(1.25) = 6280 Rs

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