Question

a spiral is made up of successive semicircle with centre alternative at A and B starting with centre at A of radius 0.5cm,1.0cm,2.0cm of such a made up of thirteen consecutive semi circle​

Answer 1

Step-by-step explanation:

let us considere radius of successive semicircles as r1, r2, r3...........

= 0.5, 1, 1.5,.............

a=0.5, d=(1-0.5)=0.5, n=13

Perimeter of successive semicircles are

$\pi \: r1 \\ \: \pi \: r2 \\ \: \pi \: r3..........$

Therefore, Perimeter of thirteen successive semicircles =

$= \pi \: r1 + \: \pi \: r2 + \: \pi \: r3.......... \\ = \pi(r1 + r2 + r3........) \\ = \pi(0.5 + 1 + 1.5........)$

= 22/7{n/2[2a+(n-1)d]}

= 22/7{13/2[2(0.5)+(13-1)0.5]}

= 22/7[13/2(1)+12(0.5)]

= 22/7[13/2(1+6)]

= 22/7[13/2(7)]

=11×13

=143 cm

Therefore, length of thirteen successive semi circles is 143cm.