Question

question 5 of 10
if the ratio between the radii of the two spheres is 3:5, what is the ratio of their volumes?
a. 27:125
b. 9:25
c. 3:25
d. 6:25

Explanation:

Step1: Recall volume formula for sphere

The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$. Let the radii of the two spheres be $r_1$ and $r_2$ with $\frac{r_1}{r_2}=\frac{3}{5}$.

Step2: Find ratio of volumes

The ratio of the volumes $V_1$ and $V_2$ of the two spheres is $\frac{V_1}{V_2}=\frac{\frac{4}{3}\pi r_1^{3}}{\frac{4}{3}\pi r_2^{3}}$. The $\frac{4}{3}\pi$ terms cancel out, leaving $\frac{V_1}{V_2}=(\frac{r_1}{r_2})^{3}$.

Step3: Substitute ratio of radii

Substitute $\frac{r_1}{r_2}=\frac{3}{5}$ into the volume - ratio formula. So $\frac{V_1}{V_2}=(\frac{3}{5})^{3}=\frac{3^{3}}{5^{3}}=\frac{27}{125}$.

Answer:

A. 27:125