Answer:
Volume of the smaller cone = 8.34 cm³
Step-by-step explanation:
"If two figures are similar, their dimensions will be proportional.
Following this rule,
Ratio of the dimensions of two cones = [tex]\frac{\text{Radius of the large cone}}{\text{Radius of the small cone}}[/tex]
= [tex]\frac{r_2}{r_1}[/tex]
= [tex]\frac{5}{2}[/tex]
= 2.5
Similarly, "ratio of the volumes of two similar figures is cube of the dimensional ratio".
Ratio of the volumes = (ratio of the dimensions)³
[tex]\frac{V_1}{V_2}=(2.5)^3[/tex]
[tex]\frac{131}{V_2}=15.625[/tex]
[tex]V_2=\frac{131}{15.625}[/tex]
= 8.384 cm³
≈ 8.4 cm³
Therefore, volume of the smaller cone is 8.4 cm³.
