Question

The figure shows a spiral made up of successive semi circles of increasing radii and centres at P and Q alternately. The first (innermost) semicircle has centre P and radius PQ is 1cm. The total length of a spiral of 10 semicircles will be

Answer 1

hey trap notion .

LET L1,L2,L3,L4,L5,L6,...........L10 BE THE LENGTH OF CONSECUTIVE SEMICIRCLE ,WITH RADIUS 1 CM ,2CM ,3 CM,......10CM... RESPECTIVELY.

THEN WE HAVE

L1=π×1CM =2πR/2CM =2π/2CM=π

L2=π×2R/2=2π2/2=2π

L3=2πR/2=6π/2=3π

SO..........
............................
L10=10π

NOW TOTAL LENGTH OF SPIRAL

=L1+L2+L3......+L10

=>π+2π+3π+....L10

NOW BY APPLYING SUM OF NTH TERM OF AP's FORMULA

Sn=n/2(a+l) ........{where a is first ,l is last and n is total no. of term in an Ap}

Sn=10/2(π+10π)

=>5×11π

=>172.8571428557 cm

approx answer 172.86cm Answer.

hope it helps you.

@Rajukumar111