Answer:
[tex] V_1 : V_2= 2197 : 729[/tex]
Step-by-step explanation:
Let the volumes of both the spheres be [tex] V_1, \:V_2[/tex] and their radii be [tex] r_1, \:r_2[/tex] respectively.
[tex] \huge r_1 : r_2= 13 : 9[/tex] (given)
[tex] \implies\huge \frac{r_1}{r_2}= \frac{13}{9}.....(1)[/tex]
[tex] \huge \frac{V_1}{V_2}=\frac{\cancel {\frac{4}{3} \pi} r_1^3}{\cancel {\frac{4}{3} \pi} r_2^3}[/tex]
[tex] \huge \frac{V_1}{V_2}=\frac{ r_1^3}{r_2^3}[/tex]
[tex]\huge \frac{V_1}{V_2}=\bigg(\frac{ r_1}{r_2}\bigg) ^3..... (2)[/tex]
From equations (1) & (2), we have:
[tex]\huge \frac{V_1}{V_2}=\bigg(\frac{13}{9}\bigg) ^3[/tex]
[tex] \huge \frac{V_1}{V_2}=\frac{2197}{729}[/tex]
[tex] \huge \therefore V_1 : V_2= 2197 : 729[/tex]
Thus, the ratio of the volumes of two spheres would be 2197 : 729.
