Question

these cones are similar. find the volume of the smaller cone. round to the nearest tenth. volume = ? cm³ volume = 131 cm³

Explanation:

Step1: Find the ratio of the radii

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

Step2: Use the volume - ratio formula for similar solids

For similar solids, the ratio of their volumes is 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. The ratio of the volumes is $(\frac{r_1}{r_2})^3$, where $r_1$ and $r_2$ are the radii of the smaller and larger cones respectively. So $\frac{V_1}{V_2}=(\frac{2}{5})^3$.

Step3: Solve for the volume of the smaller cone

We know $V_2 = 131$ $cm^3$. Then $V_1=V_2\times(\frac{2}{5})^3$. Substitute $V_2 = 131$ into the formula: $V_1=131\times\frac{8}{125}$.
$V_1=\frac{1048}{125}=8.4$ $cm^3$.

Answer:

$8.4$ $cm^3$