Question

Sergio has two similar cylindrical pots, Pot A and Pot B. The radius of Pot A is 15 inches, and the radius of Pot B is 3 inches. What is the ratio of the volume of Pot A to the volume of Pot B?

10 : 1

25 : 1

125 : 1

5 : 1

Answer 1

The volume of a cylinder is given by\[V=\pi r^2 h\]where r is the radius and h is the height. Let \[h _{A}\] be the height of Pot A and \[h _{B}\] be the height of Pot B. Because the pots are similar we know that the ratio of their heights are the same as the ratio of their radii.\[\frac{h _{B}}{h _{A}}=\frac{r _{B}}{r _{A}}=\frac{3}{15}=\frac15\]So \[h _{B}=\frac 15h _{A}\] Can you write the equation for \[\frac{V _{B}}{V _{A}}=?\]