Please help me with math!?

Question

a manufacturer produces three different sizes of cube-shaped stacking bins with edge lengths as shown.

Bin A: 6 in

Bin B: 12 in

Bin C: 18 in

find the volume of each bin

how many times greater is the edge length of bin B than the edge length of bin A? How many times greater is the volume of bin B than the volume of bin A?

explain how multiplying the edge length of a cube by a number "n" affects the volume of the cube. justify your explination.

Thanks so much for your guys' help!!!!

Answer 1

Bin A=6 X 6 X6, =216cu. in.

Bin B= 12 X 12 X 12= 1728 cu. in.

Bin C =18 X 18 X 18, =5832 cu. in.

Bin.....Side...Cube.....Ratio

.A........6........216........--

.B.......12.......1728.......8 times bigger

.C.......18.......5832......27 times bigger

ultiplying a side by 2 (from 6 to 12) makes the volume increase by 2^3

Multiplying a side by 3(from 6 to 18) makes the volume go up by 3^3

Multiplying by n makes the volume go up by n^3.

The rigorous mathematical treatment of this is as follows:

n^3=n^3

(2n)^3=8n^3, so 8n^3/n^3=8

(3n)^3=27n^3, s0 27n^3/n^2=27

(Kn)^3=K^3n^3, so K^3n^3/n^3=K^3

Whatever K, the multiplier is, K^3 will be the factor by which the volume increases

Answer 2

Ok, First off the edge length is just how much greater is each given length so for A and B, 12 is two times greater than 6 so B is 2 times greater than A in length.

The volume of a cube will be Length x Width x Height or 6 to the 3rd power for Bin A, 12 to the 3rd power for bin B

Volume of Bin A- 216 inches cubed

Volume of Bin B- 1728 inches cubed

you could also say since the length is 2x greater the volume will be 2 to the 3rd power times greater or 8 times greater.

For your last question multiplying the edge length by N just means you have to cube N and the volume is that many times greater. So with an edge length of 2n the volume will be 8 times greater than the original. Hope I was clear enough. Good Luck

Answer 3

A: 6x6x6= 216

B: 12x12x12= 1728

C: 18x18x18= 5832

x greater edge: 2

x greater volume: 8

if you multiply the edge by n, the volume increases by n^3 because to get volume, you must multiply the edge by itself three times. If you multiply the edge by 3 (like 6 to 18) the volume will be 27 times larger (3^3= 27).

Hope this helps.

Answer 4

The volume of a cube is the edge size times 3. So if the edge of bin A is 6, then you times 6 by 6 by 6 and this equals 216. 6 times 6 equals 36, and 36 times 6 equals 216. Do you understand that?

Bin B: 12 by 12 by 12 = 1728

Bin C: 18 by 18 by 18 = 5832

B is 2 times greater then A as it is double the length. To work out the volume difference, devide B with A. So, 1728 / 216 = 8. So B is 8 times greater then A.

Is this helpful to you?

Cheers Jane.