Question

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 1

Answer:

Paul's box contain $624\ in^{3}$ 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

$V=LWH$

substitute the values

$V=(4)(3)(2)=24\ in^{3}$

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 $3^{3}=27$

therefore

The volume of Paul's box is 27 times the volume of Timmy's box

$V=27(24)=648\ in^{3}$

step 3

Find the difference of the volumes of the box

$648\ in^{3}-24\ in^{3}=624\ in^{3}$

therefore

Paul's box contain $624\ in^{3}$ more than Timmy's box