The radii of two cylinders A and B are in the ratio of 5 : 6 and the heights are in the ratio of 7 : 4 respectively. The ratio of the curved surface area of cylinder B to that of A is:

The radii of two cylinders A and B are in the ratio of 5 : 6 and the heights are in the ratio of 7 : 4 respectively.

Let's assume the radii of two cylinders A and B are 5y and 6y respectively.

Let's assume the heights of two cylinders A and B are 7z and 4z respectively.

The ratio of the curved surface area of cylinder B to that of A = 

= $$\frac{ r_b\times\ h_b}{ r_a\times\ h_a}$$
= $$\frac{6y\times\ 4z}{5y\times7z}$$

= $$\frac{24}{35}$$

= 24:35