Question

Spiral is made up of successive semicircles with centres alternately at A and B starting with centre at a of radius 0.5 CM, 1.0, 1.5,...as shown in figure 5.4 what is the total length of a spiral made up of 13 consecutive semicircles

Answer 1

Answer: 143 cm

Step-by-step explanation:

Length of the semicircle = π r

L1 = 0.5π

L2 = 1π

L3 = 1.5π

L4  = 2π

we want L1 + L2 + L3 + L4 ........ L13

we need a = L1 = 0.5π

        d = L2 - L1 = O.5π

S13 = 13/2 {2*0.5π + 12(0.5π)}

        = 13/2 * 0.5π (2 + 12)         (On taking 0.5π common)

        = 13/2 * 0.5π * 14

         = 13 * 0.5 * 22/7 * 7

         = 13 * 0.5 * 22

          = 143 cm.