Question

The Right Move home-moving company has a variety of cardboard packing boxes available for use. The packing boxes shown here are similar figures. What is the volume of the larger box? Show your work and explain how you arrived at your answer by applying the scale factor rule of volume.

Two rectangular moving boxes are shown side-by-side. The first one has length of two feet, width of zero point five feet, and height of one foot. The second one has length of six feet.

Answer 1

@e.mccormick @phi @247 @IMStuck

Answer 2

First, step
1) what is the volume of the small box? can you do that ?

Answer 3

volume is area of the base times the height
or (the same thing) length*width*height

Answer 4

The first box is 1 the second I do not know because it only has one number...

Answer 5

yes, volume of the first box is 2*½*1= 1 cubic foot

Next, step. they say
boxes shown here are similar figures

that means they are the same shape, except one is bigger (or smaller)
Here is the *important* idea: if the length of the bigger box is 3 times bigger than the small box, then its width is 3 times bigger, and its height is 3 times bigger

Answer 6

The first one has length of two feet,
The second one has length of six feet.

what do you multiply the first box's length by to get the 2nd box's length ?

Answer 7

Oh! I get that now... but I don't understand what the question is tryna ask me to explain.

Answer 8

@phi

Answer 9

I think you multiply 2*3?

Answer 10

There are two ways to figure out the volume of the bigger box.

the harder way is to figure out the length, width and height (by multiply the small box's length, width and height by 3)
and then find the volume

Example: 2*3 = 6 new length
½ *3 = 3/2 new width
1*3 = 3 new height

BUT, they want you to do it a *different* way:
applying the scale factor rule of volume.

Answer 11

Here is the other way.

if you have similar figures, you can find their scale factor (the number you multiply each side by) to get the length of the other figure

any idea what our "scale factor" is ?

Answer 12

Thank you, but how do I explain this now?

Answer 13

any idea what our "scale factor" is ?

Answer 14

No...

Answer 15

@phi

Answer 16

boxes shown here are similar figures

that means they are the same shape, except one is bigger (or smaller)
Here is the *important* idea: if the length of the bigger box is 3 times bigger than the small box, then its width is 3 times bigger, and its height is 3 times bigger

do you follow this?

Answer 17

the number we multiply by (3 in the above example) is called the scale factor.

in your problem
the length of the small box is 2
the length of the big box is 6

what do we multiply 2 by to get 6 ? that number is the scale factor. what is it?

Answer 18

2*3

Answer 19

2*3 is 6

which of those is the scale factor? It is the 3
(because we use 3 times the small length to get the big length:
3 times the small boxes 2 = 6 (the big boxes length)

the scale factor is 3

once you know the scale factor you also know this:
1) the surface area of the big box is 3*3 bigger than the surface area of the small box
2) the volume of the big box is 3*3*3 bigger than the volume of the small box

use rule 2) to find the volume of the big box.