Question

Find the scale factor of a cube with volume 216 ft^3 to a cube with volume 1000 ft^3.

Answer 1

Scale factor of cube to the smaller cube is 5 : 3.

Explanation:

Ratio of the volumes of two cubes =
`\frac{\text{volume of large prism}}{\text{Volume of small prism}}`

=
`(1000)/(216)`

=
`(125)/(27)`

Scale factor of these cubes =
`\sqrt[3]{\text{ratio of the volumes of the cubes}}`

=
`\sqrt[3]{\frac{\text{volume of large prism}}{\text{Volume of small prism}}}`

=
`\sqrt[3]{(125)/(27) }`

=
`(5)/(3)`

= 5 : 3

Therefore, scale factor of cube to the smaller cube is 5 : 3.