Q. 184.5( 269 Votes )

# A spiral is made up of successive semicircles, with centres alternately at A and B,starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown inFig. 5.4. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take [Hint : Length of successive semicircles is with centres at A, B, A, B, . . .,respectively.]

Circumference of 1st semicircle = πr = 0.5π

Circumference of 2nd semicircle = πr = 1π = π

Circumference of 3rd semicircle =πr = 1.5π

It is clear that a = 0.5 π, d = 0.5π and n = 13

Hence; the length of the spiral can be calculated as follows:

= (7)

=

= 143 cm

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