Respuesta :
Answer:
The ratio is [tex]\frac{27}{343}[/tex] or 27:343
Step-by-step explanation:
The volume of cylinder is = [tex]V=\pi r^{2} h[/tex] ; where r is radius and h is height.
Given that the ratio of the heights and radii of two similar cylinders is 3 : 7.
Let r' be the radius and h' be the height of the other cylinder.
Its volume is [tex]V'=\pi r'^{2} h'[/tex]
According to the given information, we have
[tex]\frac{r}{r'}=\frac{h}{h'}=\frac{3}{7}[/tex]
Hence, we get
[tex]\frac{V}{V'}=\frac{\pi r^2h}{\pi r'^2h'}[/tex]
= [tex](\frac{3}{7})^{2} \times \frac{3}{7}[/tex]
= [tex]\frac{27}{343}[/tex]
Therefore, the ratio is 27:343
