Question

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Answer 1

Answer:

207.24 cm

Step-by-step explanation:

Let lengths of the semicircles be l₁,l₂,l₃,l₄. with centres A,B,A,B respectively.

⇒ l₁ = length of the first semicircle with centre A and radius 1 cm = π cm

⇒ l₂ = length of the second semicircle with centre B and radius 2 cm = 2π

⇒ l₃ = length of the second semicircle with centre A and radius 3 cm = 3π

Thus the numbers involved in the lengths(in cm) of semicircles are π,2π,3π

These numbers form an AP with a = π, d = 2π - π = π, n = 11.

Length of the spiral can be calculated using sum of n terms of an AP:

⇒ Sₓ = (n/2)[2a + (n - 1) * d]

        = (11/2)[2π + (11 - 1) * π]

        = (11/2)[2 * 3.14 + 10 * 3.14]

        = (11/2)[37.68]

        = 207.24.

Therefore, Length of spiral = 207.24 cm

Hope this helps!