Question

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

Answer 1

Volume of the smaller cone = 8.34 cm³

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}}`

=
`(r_2)/(r_1)`

=
`(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

`(V_1)/(V_2)=(2.5)^3`

`(131)/(V_2)=15.625`

`V_2=(131)/(15.625)`

= 8.384 cm³

≈ 8.4 cm³

Therefore, volume of the smaller cone is 8.4 cm³.