Question 48

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:

Solution

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The length of the spiral will be equal to the length of the circular arc portions of the semicircles. 
Length of the circular arc portion of a semicircle = $$\frac{22}{7}*r$$.
Length of the spiral = $$\frac{22}{7}*(0.5+1+1.5+2+...+6.5)$$
 = $$\frac{22}{7}*0.5*[1+2+3+....+13]$$
= $$\frac{11}{7}*\frac{13*14}{2}$$
=$$143$$ cm.
Therefore, option B is the right answer.

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