Answer:
Paul's box contain [tex]624\ in^{3}[/tex] more than Timmy's box
Step-by-step explanation:
step 1
Find the volume of Timmy's box
The volume of the box is equal to
[tex]V=LWH[/tex]
substitute the values
[tex]V=(4)(3)(2)=24\ in^{3}[/tex]
step 2
Find the volume of Paul's box
we know that
The scale factor is equal to 3
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
the scale factor elevated to the cube is [tex]3^{3}=27[/tex]
therefore
The volume of Paul's box is 27 times the volume of Timmy's box
[tex]V=27(24)=648\ in^{3}[/tex]
step 3
Find the difference of the volumes of the box
[tex]648\ in^{3}-24\ in^{3}=624\ in^{3}[/tex]
therefore
Paul's box contain [tex]624\ in^{3}[/tex] more than Timmy's box
