Question

A spiral is made up of successive semicircles, with radius .5 cm, 1 cm, 1.5 cm, ….. What is the total length of the spiral made up of thirteen consecutive semicircles? (Take π=22/7)

Answer 1

Answer:

Let L₁, L₂, L₃, L₄, ........, L₁₃ be the lengths of semicircles of radii 0.5 cm, 1 cm, 2 cm .... and 13/2 cm respectively.

Then, we have

L₁ = π × 0.5 = π/2 cm,

L₂ = π × 1 = 2(π/2) cm,

L₃ = π × 1.5 = 3(π/2) cm,

L₄ =  π × 2 = 4(π/2) cm,

_________________

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L₁₃ =  π × 13/2 = 13(π/2) cm,

Therefore,

Total length of the spiral

= L₁ + L₂ + L₃ + L₄ + ....., + L₁₃

= [π/2 + 2(π/2) + 3(π/2) + 4(π/2) + ......., + 13(π/2)] cm

= π/2(1 + 2 + 3 + 4 + ........ + 13) cm

= π/2 × 13/2 × (1 + 13) cm

= (1/2 × 22/7 × 13/2 × 14) cm

= 143 cm.

Hence, the required length of the spiral is 143 cm.

Answer 2

Answer:

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Step-by-step explanation:

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