Question

15. Concentric circles of radii 1, 2, 3,....., 100cm are drawn. The interior of the smallest circle is coloured red and the angular
regions are coloured alternately green and red, so that no two adjacent regions are of the same colour. Then find the total area of
green regions in sq.cm.​

Answer 1

Answer:

5050 π  cm²

15871.4 cm²

Step-by-step explanation:

Smallest  circle is colured Red

Then Area of Green region for 1st two Circles=  π2² - π1²

= π * 1 * 3

Then Area of next green region =  π4² - π3²  

= π * 1 * 7

and

so on

last green region area = π100² - π99²  

=  π * 1 * 199

Total Green area

=π * 1 * 3 + π * 1 * 7 + π * 1 * 11  +..................................................+ π * 1 * 199

=π ( 3 + 7 + 11 +.......................................+ 199)

a = 3  n = 50  d = 4

S = (50/2)(3 + 199) = 50 * 101

Area of green region = 50 * 101 * π  cm² = 5050 π  cm²

= 15871.4 cm²