Question

Help, Please!! 6th-grade math...
(Picture down under this in the comments)

Answer 1

We just learned yesterday to do it with fractions, I know you do BxWxH but after that I'm kinda stuck

Answer 2

Does someone know how to do this? Its due tonight and I have Cross Country at 3

Answer 3

Well since no one is deciding to help you, Imma do it smh.

This is for number 10.
\[B*W*H\]Since it's a cube, all sides are 1/2 units

Answer 4

ok

Answer 5

So the equation would be:
\[\frac{ 1 }{ 2 }*\frac{ 1 }{ 2 }*\frac{ 1 }{ 2 }\]What is 1/2 * 1/2 * 1/2 then?

Answer 6

1/8th?

Answer 7

Yes. So now for Part B of 10 (the 1/3 unit).

Just like before:
\[\frac{ 1 }{ 3 }*\frac{ 1 }{ 3 }*\frac{ 1 }{ 3 }\]What is that then?

Answer 8

ok, one sec

Answer 9

1/27th?

Answer 10

Yes. So for Part A on 10:

You have 1/8 units

Part B:

You have 1/27 units

The cube you are filling has a volume of 8 cubic units.

Answer 11

ok

Answer 12

And so-

we started with 1/2 unit for Part A

1/3 unit for Part B

The rectangular prism you are filling is 8 cubic units-

How many times does 1/2 go into 8?

Answer 13

16

Answer 14

Yes.

And how many times does 1/3 go into 8?

Answer 15

24

Answer 16

Yes.

Now it states in question 10:

"How many more of the cubes with 1/3 unit side lengths than cubes with 1/2 unite side lengths are needed to fill the prism?"

It's just asking for the difference between 24 and 16. Just subtract those two.
\[24-16\]

Answer 17

8

Answer 18

Yes. So there is your answer for number 10: 8

Now for number 11.

I'll just explain why:

It takes more cubes with lengths 1/3 to fill the prism because 1/3 is smaller than 1/2.

Answer 19

ok, thanks

Answer 20

You're welcome

Answer 21

So your rectangular prism has a volume of 8

You then calculated that the volume of a cube with side lengths 1/2 would be 1/8

and that the volume of a cube with side lengths 1/3 would be 1/27


Now you're filling up this rectangular prism with as many cubes with side lengths 1/2

and then you empty it out and fill it up with the 1/3 side length cubes

Answer 22

So to find out how many cubes would fit into your rectangular prism, you have to divide

not by the side lengths but by the volumes

this is where you went wrong earlier

Answer 23

so how many cubes with side length of 1/2 can fit into the prism?

The volume of a cube with side length 1/2 is 1/8 as you found earlier

\( 8 \div \dfrac{1}{8} = ?\)

remember

\( a\div \dfrac{b}{c} = a \times \dfrac{c}{b}\)

so essentially

\( 8 \div \dfrac{1}{8} = 8\times 8 = ??\)

What is 8 * 8 = ??

That's how many cubes with side length of 1/2 can fit in the prism

Answer 24

Similarly, for the cube with side length of 1/3. It has a volume of 1/27 like you found earlier

So to find out how many of those cubes would fit in

\( 8 \div \dfrac{1}{27}= ?\)

So what is 8 * 27 = ?

Answer 25

And then find the difference between those two numbers you calculate

That's how many more cubes with sides of 1/3 there are compared to the cube with sides of 1/2