Timmy has a box which is 3" wide, 4" long, and 2" high. Paul has a box whose dimensions are three times as wide, long, and high. How much more volume does Paul's contain?

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