The ratio of the volume of two cylinders is 7 : 3 and the ratio of their heights is 7 : 9. If the area of the base of the second cylinder is 154 cm2, then what will be the radius (in cm) of the first cylinder?

Ratio of heights = 7 : 9

Let height of first cylinder = $$h_1=7$$ cm and second cylinder = $$h_2=9$$ cm

Let radius of first cylinder = $$r_1$$ cm and second cylinder = $$r_2$$ cm

Area of base of second cylinder = $$\pi(r_2)^2=154$$

=> $$\frac{22}{7}(r_2)^2=154$$

=> $$(r_2)^2=154\times\frac{7}{22}=49$$

$$\therefore$$ Ratio of volumes = 7 : 3

=> $$\frac{\pi(r_1)^2h_1}{\pi(r_2)^2h_2}=\frac{7}{3}$$ 

=> $$\frac{(r_1)^2\times7}{49\times9}=\frac{7}{3}$$

=> $$(r_1)^2=\frac{7}{3}\times63=147$$

=> $$r_1=\sqrt{147}=7\sqrt3$$ cm

=> Ans - (D)