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small cubes with edge lengths of 1/4 will be..

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RASTA aktiv_icon

18:26 Uhr, 17.05.2022

Tag!
Small cubes with edge lenghts of

\frac{1}{4}

will be packed into the right rectangle prosm. how many small cubes are needed to fill the right rectangular prism

the formula for a right rectangular prism is

A = 2

(wl+hl+hw)
can

i

use this formula

l = 4 \frac{1}{2}

w = 5

h = 3 \frac{1}{4}

in

and then plug in the dimensions given and solve for the area?
then see how many cubs of

\frac{1}{4}

in are needed to fill the area?

pivot aktiv_icon

18:31 Uhr, 17.05.2022

Hello,

is there a picture to this exercise? If yes, please attach it.
As far as I see you have to fill the rectangular prism with the cubes. So you need the formula for the volume.

greetings,
pivot

RASTA aktiv_icon

18:45 Uhr, 17.05.2022

Oh, it is volume then. okay,

V = l \cdot w \cdot h

V = 4 \frac{1}{2} \cdot 5 \in \cdot 3 \frac{1}{4}

\frac{9}{2} \cdot 5 \cdot \frac{13}{4}

Volume

= 73.13 \in^{3}

so now, how doi calculate how many cubas fit in this space?

can

i

perform division, as in,

73 . \frac{13}{1} / 4

is this correct?

pivot aktiv_icon

18:57 Uhr, 17.05.2022

You approach is too complicated. The length of a cube is

\frac{1}{4} .

How many cubes fits in a row with a height of

3 \frac{1}{4} = \frac{13}{4}

?
How many cubes fits in a row with a length of

5 = \frac{20}{4}

?
How many cubes fits in a row with a width of

4 \frac{1}{2} = \frac{18}{4}

?

Then use that the volume is

V = h \cdot l \cdot h

>>9/2⋅5⋅13/4

Volume =73.13∈3<<

Here it is better to keep the fractions:

9 / 2 \cdot 5 \cdot 13 / 4 = 18 / 4 \cdot 20 / 4 \cdot 13 / 4

And you can go on to replace the numbers by the corresponding number of cubes.

RASTA aktiv_icon

19:05 Uhr, 17.05.2022

you wrtoe

4 \frac{1}{2} = \frac{18}{4}

??????

you meant

\frac{9}{2},

nicht war?

pivot aktiv_icon

19:09 Uhr, 17.05.2022

I've made an edit which refers to your approach. Have a look.

Isn't 18/4=9/2?

RASTA aktiv_icon

19:09 Uhr, 17.05.2022

and pivot, please, you said my approach was too complicated. but that does not mean it is wrong, or is it?

if it is not?
then, can I divide

73.13

\frac{1}{4}

to get the amount of cubes needed, please, confirm this or deny it, please, before I act on your proposed way.

pivot aktiv_icon

19:10 Uhr, 17.05.2022

I've made an edit. Have a look. (18:57)

RASTA aktiv_icon

19:47 Uhr, 17.05.2022

pivot, I like your approach, this one
how many

\frac{1}{4}

in cubes fit in a row with a height of

3 \frac{1}{4}

?

what operation Must I do to solve this?

is it division, like in

\frac{13}{4}

\frac{1}{4}

pivot aktiv_icon

20:04 Uhr, 17.05.2022

Yes. And

13 / 4 \div 1 / 4 = 13 / 4 * 4 / 1 = \frac{13}{4} * 4

I post a slightly other way, although we are not finished yet with this.

The volume of the small cube with the side length 1/4 is

\frac{1}{4^{3}}

The volume of the big cube is

18 / 4 \cdot 20 / 4 \cdot 13 / 4 = \frac{18 \cdot 20 \cdot 13}{4^{3}}

Therefore

18 \cdot 20 \cdot 13

small cubes fit in the big cube.

RASTA aktiv_icon

20:20 Uhr, 17.05.2022

Allow me to follow your way to the end.

\frac{13}{4}

\frac{1}{4} = \frac{13}{4} \cdot \frac{4}{1} = \frac{52}{4} = 13

\frac{1}{4}

5 = \frac{1}{4} \cdot \frac{5}{1} = \frac{5}{4} = 1.2

\frac{9}{2}

\frac{1}{4} = \frac{9}{2} \cdot \frac{4}{1} = \frac{36}{2} = 18

so I will add all the results

13 + 1.2 + 18 = 32.20

is this correct, if so, then what is next?

RASTA aktiv_icon

20:34 Uhr, 17.05.2022

I am missiong something.

i

am sorry. ich verstehe nicht

RASTA aktiv_icon

20:38 Uhr, 17.05.2022

you told me miy way was too complicated then you psoted how many

\frac{1}{4}

in cubes fit in a row with a height of

3 \frac{1}{4} =

we agreed it was

\frac{13}{4}

and we did this for the three dimensions

5 \cdot \frac{4}{1} = 20

\frac{9}{2}

\frac{1}{4} = \frac{9}{2} \cdot \frac{4}{1} = \frac{36}{3} = 12

so we have

\frac{13}{4}, 20, 12,

what do we do with these?. I lost you here.

RASTA aktiv_icon

20:45 Uhr, 17.05.2022

isn't this way even better?

lets find the volume of the small cube

V = l \cdot w \cdot h

= \frac{1}{4} \cdot \frac{1}{4} \cdot \frac{1}{4}

\frac{1}{64}

volume of the smaoll cube

\frac{1}{64}

let's find the volume of the bigger rectangular prism

V = l \cdot w \cdot h

V = \frac{4 \cdot 1}{2} \cdot 5 \cdot \frac{3 \cdot 3}{4} = \frac{675}{8}

now,

\frac{675}{8} \cdot \frac{64}{1} = 5400

5,400

cubes of

\frac{1}{4}

in will ft in to the rectangular prism.

Isn't this a better way?

pivot aktiv_icon

20:48 Uhr, 17.05.2022

Second line:

You have to divide it always by 1/4 and not the other way round. Thus we have 5÷1/4=5*4=20.

The rest is right.

RASTA aktiv_icon

20:56 Uhr, 17.05.2022

You have to divide it always by

\frac{1}{4}

and not the other way round. Thus we have 5÷1/4=5*4=20.

but pivot doesn't division turns into multiplication ????

as in,

5 ÷

\frac{1}{4}

becomes

5 \cdot \frac{4}{1}

which in the end is the same thing

= 20

pivot aktiv_icon

21:08 Uhr, 17.05.2022

Xes, you're right.

pivot aktiv_icon

21:25 Uhr, 17.05.2022

But it is not the same as

¼ \div 5 = 1 / 20 .

RASTA aktiv_icon

22:03 Uhr, 17.05.2022

Alright. Ich jetzt verstehe. thanks, pivot!.

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