The volume of the rectangular prism is
[tex]l \times b \times h =112 cm^3 [/tex]
Let the scale factor be
[tex]k[/tex]
If we multiply each of the dimensions by k, then we have,
[tex]lk, bk, hk[/tex]
as our new dimensions
Then the new volume is
[tex]lbh \times k^3 = 1.75 cm^3 [/tex]
But
[tex]lbh = 112 cm^3 [/tex]
[tex]\Rightarrow 112 \times k^3 = 1.75 cm^3 [/tex]
[tex]\Rightarrow k^3 =\frac{1.75}{112} [/tex]
[tex]\Rightarrow k^3 =\frac{1}{64} [/tex]
[tex]\Rightarrow k=\sqrt(\frac{1}{64})[/tex]
[tex]\Rightarrow k=\frac{1}{8}[/tex]
[tex] <B>Hence the scale factor is</B> [/tex]
[tex]\frac{1}{8}[/tex]
