these cones are similar. find the volume of the smaller cone. round to the nearest tenth. volume = ? cm³…

Explanation:

Step1: Find the ratio of the radii

The ratio of the radii of the smaller cone to the larger cone is $\frac{r_1}{r_2}=\frac{2}{5}$.

Step2: Use the volume - ratio formula for similar solids

For similar solids, the ratio of their volumes is equal to the cube of the ratio of their corresponding linear dimensions. Let $V_1$ be the volume of the smaller cone and $V_2$ be the volume of the larger cone. Then $\frac{V_1}{V_2}=(\frac{r_1}{r_2})^3$. We know $V_2 = 131$ $cm^3$ and $\frac{r_1}{r_2}=\frac{2}{5}$, so $\frac{V_1}{131}=(\frac{2}{5})^3$.

Step3: Calculate $V_1$

First, $(\frac{2}{5})^3=\frac{2^3}{5^3}=\frac{8}{125}$. Then $V_1=\frac{8}{125}\times131$. $V_1=\frac{1048}{125}=8.384\approx8.4$ $cm^3$.

Answer:

$8.4$ $cm^3$