A wire would enclose an area of 1936 m^2, if it is bent to a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters?
A. 1096
B. 1111
C. 1243
D. 2486
GATE 2018 · General Aptitude · Geometry · medium
Answer: Sum of areas = 1089 + 154 = 1243 m^2 (Option C)
Find original wire length: side = sqrt(1936) = 44 m; total wire L = 4 x 44 = 176 m
Split wire in ratio 3:1: shorter piece = 176/4 = 44 m; longer piece = 3 x 44 = 132 m
Area of new square from long piece: side = 132/4 = 33 m; area_square = 33^2 = 1089 m^2
Radius of circle from short piece: 2 * pi * r = 44 => r = 44 / (2 * 3.14159) = 7.003 m
Area of circle and total sum: area_circle = 3.14159 x (7.003)^2 = 3.14159 x 49.04 = 154.06 m^2; Total = 1089 + 154 = 1243 m^2