Question

These cones are similar. find the volume of the smaller cone. round to the nearest tenth.

Answer 1

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 = $\frac{\text{Radius of the large cone}}{\text{Radius of the small cone}}$

                                                               = $\frac{r_2}{r_1}$

                                                               = $\frac{5}{2}$

                                                               = 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

$\frac{V_1}{V_2}=(2.5)^3$

$\frac{131}{V_2}=15.625$

$V_2=\frac{131}{15.625}$

    = 8.384 cm³  

    ≈ 8.4 cm³

Therefore, volume of the smaller cone is 8.4 cm³.