Question

please answer this question correctly...coz tomorrow is my maths exam

Answer 1

let l1,l2,l3,l4........l13 be the lengths (circumference)of semi circles of radii
R1=0.5cm, r2=1.0, r3=1.5cm, r4=2.0cm, r5=2.5cm......respectively. then,

l1= πr1=π×0.5cm=π/2cm

l2=πr2=π×1cm=2(π/2)cm

l3=πr3=π×3/2cm=3(π/2)cm

l4=πr4=π×2cm=4(π/2)cm
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l13=πr13=π×13/2cm=13(π/2)cm

therefore, total length of the spiral =l1+l2+l3+.......l13

={π/2+2(π/2)+3(π/2)+.........+13(π/2)}cm

=π/2(1+2+3+........13) cm

=π/2×13/2(1+13)cm __________[using an=n/2(a+l)]

=π/2×13/2×14cm= 1/2×22/7×13×7cm= 143cm

ANS=143cm


HOPE IT WILL HELP YOU......