Question

The sum of diameter of two circles is 112 cm and the sum of their areas is 5236 cm² Find the radii of the two circles. 

Answer 1

Sum of the diameters = 112 cm 

Therefore, sum of the radii = `112/2` cm = 56 cm

If r is the radius of one circle, radius of other circle is (56 - r)

Sum of the areas = π r² + π (56 - r)²  

⇒ π r² + π (56 - r)² = 5236

⇒ π r² + π (3136 - 112 r + r²) = 5236

⇒ (r² + 3136 - 112 r + r²) × `22/7` = 5236

⇒ 2r² - 112r + 3136 = 1666 

⇒ 2r² - 112r + 3136  - 1666 = 0

⇒  2r² - 112r + 1470 = 0

⇒ r² - 56r + 735 = 0

⇒ (r - 35)(r - 21) = 0

⇒ r = 35 , r = 21

Therefore, radii of the two circles is 35 cm and 21 cm