Question

PLEASE HELP! What is the ratio of the volumes of two spheres, if the ratio of their radii is 13: 9

Answer 1

Answer:

2197:729

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Answer 2

Answer:

$V_1 : V_2= 2197 : 729$

Step-by-step explanation:

Let the volumes of both the spheres be $V_1, \:V_2$ and their radii be $r_1, \:r_2$ respectively.

$\huge r_1 : r_2= 13 : 9$ (given)

$\implies\huge \frac{r_1}{r_2}= \frac{13}{9}.....(1)$

$\huge \frac{V_1}{V_2}=\frac{\cancel {\frac{4}{3} \pi} r_1^3}{\cancel {\frac{4}{3} \pi} r_2^3}$

$\huge \frac{V_1}{V_2}=\frac{ r_1^3}{r_2^3}$

$\huge \frac{V_1}{V_2}=\bigg(\frac{ r_1}{r_2}\bigg) ^3..... (2)$

From equations (1) & (2), we have:

$\huge \frac{V_1}{V_2}=\bigg(\frac{13}{9}\bigg) ^3$

$\huge \frac{V_1}{V_2}=\frac{2197}{729}$

$\huge \therefore V_1 : V_2= 2197 : 729$

Thus, the ratio of the volumes of two spheres would be 2197 : 729.