Q10 of 35 Page 311

Anwar bibi has spent Rs. 2664 at the rate of Rs. 18.50 per meter for fencing of her semicircular land. Let us write by calculating how much cost it will take, if she makes the semicircular land plough at the rate of Rs. 32 per sq. meter.

cost of fencing semicircular land = Rs 2664


Rate is fencing = Rs 18.50/m


Let r be the radius of semicircular field


Then, perimeter of this field = (πr + 2r) m where r is the radius of the circle


Cost of fencing semicircular land = perimeter of the semicircular land × rate of ploughing per sq meter


2664 = (πr + 2r) × 18.50


⇒ 2664 = r( π + 2) × 18.50 (taking r common from the bracket)


⇒ (putting π as)


⇒


⇒


⇒ r = 28 m


Perimeter of the semicircular land = r ( π + 2) where r is the radius



=


= 144 m


Area of semicircular field = where r is the radius


=


= 1232 m2


Cost of ploughing the field = area of field × rate of ploughing per square meter


= 1232 × 32 = Rs 39,424


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