Question

a rectangular prism has a volume of 112 cm every dimension of the rectangular prism is multiplied by a scale factor and the new volume is 1.75 cm3 . what was the scale factor

Answer 1

The volume of the rectangular prism is

$l \times b \times h =112 cm^3$

Let the scale factor be

$k$

If we multiply each of the dimensions by k, then we have,

$lk, bk, hk$

as our new dimensions

Then the new volume is

$lbh \times k^3 = 1.75 cm^3$

But

$lbh = 112 cm^3$

$\Rightarrow 112 \times k^3 = 1.75 cm^3$

$\Rightarrow k^3 =\frac{1.75}{112}$

$\Rightarrow k^3 =\frac{1}{64}$

$\Rightarrow k=\sqrt(\frac{1}{64})$

$\Rightarrow k=\frac{1}{8}$

$Hence the scale factor is$

$\frac{1}{8}$