The volumes of spheres A and B are in the ratio 125 : 64. If the sum of radii of A and B is 36 cm,then the surface area (in $$cm^{2}$$) of A is:

The ratio of the volume of the Sphere A and B = 125 : 64

$$\frac{4}{3} \times \pi \times r_a^3 : $$\frac{4}{3} \times \pi \times r_b^3$$ = 125 : 64

$$r_a^3 : r_b^3$$ = 125 : 64

$$(\frac{r_a}{r_b})^3 = \frac{125}{64}$$

$$\frac{r_a}{r_b} = \frac{5}{4}$$

$$4r_a = 5r_b$$ ---(1)

($$r_a + r_b = 36$$)

Put the value of $$r_b$$ in eq (1),

$$4r_a = 5(36 - r_a)$$

$$4r_a + 5r_a = 180$$

$$r_a$$ = 180/9 = 20 cm

Surface area of the A = $$4 \pi r^2$$

= $$4 \times \pi \times 20 \times 20 = 1600\pi$$