The ratio of volumes of two spheres A and B is 27 : 125. If the sum of their radii is 56 cm, then find the surface area of A?

5544 cm²

                                        A          :              B

Ratio of volumes       \(\frac{4}{3}\) \(\pi \) r_A³          :            \(\frac{4}{3}\) \(\pi \) r_B³

⇒ r_A³ :  r_B³ = 27 : 125

⇒ r_A :  r_B = 3 : 5

sum of radius (r_A + r_B) = 32 cm

⇒ 8x = 56 cm

⇒  x = 7

r_A = 3 × 7 = 21 cm

surface area = 4\(\pi \)r²

                    = 4 × \(\frac{22}{7}\) × 21 × 21  = 5544 cm²