Indian Institute of Foreign Trade 2008 Solved Paper

Question : 48 of 150

Marks: +1, -0

A spiral is made up of 13 successive semicircles, with centres alternately at A and B, starting with the centre at A. The radii of semicircles thus developed are 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm and so on. The total length of the spiral is:

144 cm
143 cm
174 cm
None of the above

Validate

Solution:

The length of the spiral will be equal to the length of the circular arc portions of the semicircles

=22/7∗r

Length of the spiral

=2/77∗(0.5+1+1.5+2+..1+6.5)

=\;\;{22}/{7}∗0.5∗[1+2+3+. . ..+13]

=11/7∗{13∗14}/2

=143

cm
Therefore, option B is the right answer.

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