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\sqrt2 ft. and cost of construction is Rs.100 per sq. ft. Find the lowest possible cost to construct 50% of the total road.

Xavier Aptitude Test 2015 Paper

Question : 57 of 113

Marks: +1, -0

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.

Solution:

(b) Perimeter of the square field = 200 ft
Side of the square field with perimeter = 50 ft.
Length of diagonal of the square = 50

√2

ft.
For least cost of construction, inner radius of the circular road = 25

√2

ft.
Then, outer radius = 25

√2

+ 7

√2

= 32

√2

ft.
The area of the circular road =

{22}/{7} \×[(32 \√{2})^{2}-(25 \√{2})^{2}\ ]= {22}/{7}× 2 \×(32+25)

\×(32-25)=2508 {sq.} \ {ft}

Cost of construction per sq. ft = Rs.100
Minimum cost to construct 50% of the whole road

=\ {250800}/{2}=125,400

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