The respective ratio of radii of two right circular cylinders (A and B) is 3 : 2. The respective ratio of volumes of cylinders A and B is 9 : 7, then what are the heights of cylinders A and B ?

Volume of a cylinder = $$\pi r^2 h$$
where r and h are radius and height of the cylinder respectively.
Let $$r_1$$ , $$h_1$$ , $$r_2$$ and $$h_2$$ be the radius and heights of the two cylinders respectively.
$$\pi (r_1)^2 h_1$$ : $$\pi (r_2)^2 h_2$$ = 9 : 7 ------------- 1
Ratio of radii $$r_1 : r_2 = 3 : 2$$
Ratio of square of radii = 9 : 4
Replacing the ratio of radii in 1
$$9h_1 : 4h_2$$ $$= 9: 7$$
$$h_1 : h_2$$ $$= (9\times 4) : (7\times 9)= 4 : 7$$
Option B is the correct answer.