Q. 45.0( 2 Votes )


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

Answer :


https://gs-post-images.grdp.co/user_files/63094/15050/images/extra-12_files/5e.gif

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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