Question

What is the similarity ratio of a cube with volume 216 m³ to a cube with volume 2744 m³

A. 3:7
B. 7:3
C. 36:196
D. 196:36

Answer 1

A. 3:7

Explanation:

The volume of the smaller cube is 216 m³.

The volume of the larger cube is 2744 m³

Let the similarity ratio be
`l:L`

The volume of these two cubes are in the ratio:

`l^3:L^3=216:2744`

This implies that:

`((l)/(L))^3 =(216)/(2744)`

We take the cube root of both sides to obtain:

`(l)/(L) =\sqrt[3]{(216)/(2744)}`

`(l)/(L) =(6)/(14)`

This simplifies to:

`(l)/(L) =(3)/(7)`

Therefore the ratio is 3:7