Question

What is the scale factor of a cube with volume 1,331 ft.3 to a cube with volume 85,184 ft.3?

Answer 1

I know the answer is 1/4, but all I get is 1/64 when I use a calculator.

Answer 2

take the cube root of each, that will give the side length

then the scaling factor is the ratio of linear measurements or ratio of he side measurements.

Answer 3

so find the ration of the side lengths, right?

Answer 4

hmmm lemme fix that

Answer 5

\(\bf \large \cfrac{{\color{blue}{ volume }}}{{\color{brown}{ volume }}}=\cfrac{{\color{blue}{ side}}^3}{{\color{brown}{ side}}^3}\implies
\cfrac{\sqrt[3]{{\color{blue}{ volume }}}}{\sqrt[3]{{\color{brown}{ volume }}}}=\cfrac{{\color{blue}{ side}}}{{\color{brown}{ side}}}\impliedby ratio\)

use the values given then

Answer 6

Ok, thanks this is very helpful. I will add this to my formula list

Answer 7

yw