Question

Class 10 ch 5 arithmetic progression.

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Answer 1

Answer:

143 cm

Step-by-step explanation:

Circumference of 1st semicircle = 0.5π

Circumference of 2nd semicircle = π

Circumference of 3rd semicircle = 1.5π

Thus, a = 0.5 π, d = 0.5π and n = 13

{13 consecutive semicircles}

Length of the spiral calculated as :

S = (n/2)[2a + (n - 1) * d]

  = (13/2)[2 * 0.5π + (13 - 1) * 0.5π]

 = (13/2)[π + 6π]

 = (13/2)[7π]

 = (13/2)[7 * 22/7]

= (13/2)[22]

= 143

Therefore,

Total Length = 143 cm.

Hope it helps!