Question

Two cylindrical drums have their volumes in ratio 8:27

Answer 1

$$V=\pi r^2 h$$

Suppose that these two cylinders are similar

$$r_1/r_2=h_1/h_2$$

Then

$$\dfrac{V_1}{V_2}=\dfrac{\pi r_1^2h_1 }{\pi r_2^2h_2}=(\dfrac{r_1}{r_2})^3=\dfrac{8}{27}$$

$$\dfrac{r_1}{r_2}=\dfrac{2}{3}=\dfrac{h_1}{h_2}$$