Question

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

Explanation:

Step1: Recall sphere volume formula

The volume of a sphere is $V = \frac{4}{3}\pi r^3$, where $r$ is the radius.

Step2: Assign radii values

Let the radii be $r_1=3$ and $r_2=5$.

Step3: Compute volume ratio

$$\begin{align*} \frac{V_1}{V_2}&=\frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3}\\ &=\frac{r_1^3}{r_2^3}\\ &=\frac{3^3}{5^3}\\ &=\frac{27}{125} \end{align*}$$

Answer:

D. 27:125