1. A circular road is constructed outside a square field. The perimeter of the square field is 200 ft. If the width of the road is 7√2 ft. and cost of construction is Rs. 100 per sq.ft. Find the lowest possible cost to construct 50% of the total road.
Write Comment
Comments
By: anil on 05 May 2019 02.37 am
Perimeter of square ABCD = 200 ft => AB = $$frac{200}{4} = 50$$ ft => $$DB = sqrt{50^2 + 50^2} = 50 sqrt{2}$$ ft => $$BO = r = frac{50 sqrt{2}}{2} = 25 sqrt{2}$$ ft Width of the road = BX = $$7 sqrt{2}$$ ft => $$BX = R = 25 sqrt{2} + 7 sqrt{2} = 32 sqrt{2}$$ Area of bigger circle = $$pi R^2 = pi (32 sqrt{2})^2 = 2048 pi$$ sq. ft Area of smaller circle = $$pi r^2 = pi (25 sqrt{2})^2 = 1250 pi$$ sq. ft => Area of road = $$2048 pi - 1250 pi = 798 imes frac{22}{7} = 2508$$ sq. ft But we have to calculate cost of construction of 50% road. Required Construction = $$frac{2508}{2} = 1254$$ sq. ft $$ herefore$$ Cost of 1254 ft = $$1254 imes 100 = Rs. 1,25,400$$
Terms And Service:We do not guarantee the accuracy of available data ..We Provide Information On Public Data.. Please consult an expert before using this data for commercial or personal use