Question

A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A of radii 0.5, 1.0 cm, 1.5 cm, 2.0 cm, ……… as shown in figure. What is the total length of such a spiral made up of thirteen consecutive semicircles?

Answer 1

Semi-perimeter of circle = πr

I₁ = π(0.5)

I₂ = π(1) = π cm

I₃ = π(1.5) =

Therefore, I₁, I₂, I₃ ,i.e. the lengths of the semi-circles are in an A.P.,

S₁₃ =?

We know that the sum of n terms of an a A.P. is given by

= 143

Therefore, the length of such spiral of thirteen consecutive semi-circles will be 143 cm.