Question

A circular road is constructed outside a square field. The perimeter of the square field is $200	ext{ ft}$. If the width of the road is $7\sqrt{2}	ext{ ft}$ and cost of construction is Rs. $100$ per sq.ft., find the lowest possible cost to construct $50\%$ of the total road.

Accepted Answer

B. Side of square $s = 200/4 = 50	ext{ ft}$. Distance from center to corner = $\frac{50\sqrt{2}}{2} = 25\sqrt{2}	ext{ ft}$. To construct a road outside the square field, inner radius $r = 25\sqrt{2}	ext{ ft}$. Outer radius $R = 25\sqrt{2} + 7\sqrt{2} = 32\sqrt{2}	ext{ ft}$. Area of circular road = $\pi (R^2 - r^2) = \pi [(32\sqrt{2})^2 - (25\sqrt{2})^2] = \pi [2048 - 1250] = 798\pi	ext{ sq.ft.}$ Taking $\pi = \frac{22}{7}$, Area = $798 	imes \frac{22}{7} = 2508	ext{ sq.ft.}$ Area of $50\%$ road = $2508 / 2 = 1254	ext{ sq.ft.}$ Cost = $1254 	imes 100 =$ Rs. $125,400$.

Cost of Road Construction Outside Square Field

Explanation

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