Question

A spiral formed by semicircles have radii 0.5,1.0,1.5.... respectively.What is the total length of 13 semicircles?

Answer 1

Circumference of first semicircle = πr = 0.5π

Circumference of second semicircle = πr = 1π = π

Circumference of third semicircle =πr = 1.5π





It is clear that a = 0.5 π, d = 0.5π and n = 13

Hence; length of spiral can be calculated as follows:

sum of n terms
10 arithmetic progression exercise solution

Answer 2

Length of one semicircle = πr

So, length of 13 semicircles is π{0.5}+π{1}+π{1.5}+...+π{6.5}

=π{0.5+1+1.5+...+6.5}

{sum of AP}

=π{0.5+6.5}/2