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Here radius of semi circular grassy plot = r
And
Radius of semi circular grassy plot with 4 m wide path = R = ( r + 4 ) m
Given : Circumference of semi circular grassy plot = 11447 m
We know : Circumference of semicircle = πr + 2 r , So
⇒ r π + 2 = 11447⇒ r 227 + 2 = 11447⇒ r 22 + 147 = 11447⇒ r 367 = 11447⇒ r = 11447 × 736⇒ r =31.78
So,
Radius of semi circular grassy plot with 4 m wide path = R = ( r + 4 ) = 31.78 + 4 = 35.78 m
1 ) Area of path = Area of semi circular grassy plot with 4 m wide path - Area of semi circular grassy plot
We know area of semicircle = π r22
Area of path =227 ×35.7822 - 227 ×31.7822 = 11 ×1280.20847 - 11 ×1009.96847 = 2011.756 - 1587.0932 = 424.6628≈424.66 m2 ( Ans )
2 ) Given : Rate of gravelling the path at Rs1.50 per metre square.
So,
Cost of gravelling the path at the = 424.66 ×1.50 = Rs .636.99 ≈
Rs. 637 ( Ans ) 3 ) Rate of trufing the plot at the rate of 45 paise per m.
So,
Cost of trufing the plot = 1587.0932 × 0.45 = Rs .714.19194 ≈
Rs. 714.20