GATE Mechanical Engineering (ME) 2018 Shift 2 Solved Paper

Question : 9 of 65

Marks: +1, -0

A wire would enclose an area of

1936 {m}^{2}

, if it is bent into 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?

1096
1111
1243
2486

Validate

Solution:

Area

=1936 {m}^{2}

a^{2} \;\; =1936 {m}^{2}

a \;\; =44 {m}

Length of wire

=4 a

=4 × 44=176 {m}

part-1 length

=3 × 44=132 {m}

part-2 length

=1 × 44=44 {m}

Long wire is bent in square.

4 a=132

a=33 {m}

Area of square

=33^{2}=1089 {m}^{2}

Now, small wire is bent in circle,
So,

π D=44

\;{22}/{7} × D=44

D=44

Area of circle

=\;{π}/{4} × D^{2}=\;{π}/{4} × 14^{2}

=153.94 {m}^{2}

Total area enclosed = Area of square

+

Area of circle

=1089+153.94

=1242.97 ≈ 1243 {m}^{2}

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