Question

What are the sides of a rectangular prism increased by if the volume increases from 54 mm3 to 3456 mm3?

Answer 1

Answer:

The sides of the original rectangular prism have been increased by a scale factor of 4

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x---> volume of the increased rectangular prism

y---> volume of the original rectangular prism

$z^{3}=\frac{x}{y}$

substitute

$z^{3}=\frac{3,456}{54}=64$

$z=4$ -----> the scale factor

therefore

The sides of the original rectangular prism have been increased by a scale factor of 4