Question

I'm having trouble solving this:
Corry collects cube containers. She fills them with water and pours them into a rectangular prism. She was playing with them and discovered something interesting. She had three cube containers. One cube was 1 inch by 1 inch by 1 inch. A second cube was 2 inches by 2 inches by 2 inches and a third cube was 3 inches by 3inches by 3 inches.
She filled all three with water. Then Corry poured all three cubes into a rectangular prism filling it exactly! The rectangular prism has a square base with a side length (1+2+3 = 6) inches and the height is 1 inch.
Corry wonders whether she has found a pattern. Investigate using more cube containers to fill square base prisms with heights of 1 in. Describe any conjectures you discover.

Answer 1

Corry's conjecture is right, and the volume follows a pattern

The volume of a cube of side length l is:

$V = l^3$

For the first cube of length 1 in, the volume is:

$V = 1^3$

$V = 1$

For the second cube of length 2 in, the volume is:

$V = 2^3$

$V = 8$

For the third cube of length 1 in, the volume is:

$V = 3^3$

$V = 27$

So, the total volume is:

$Total =1 + 8 + 27$

$Total =36$

The volume of a rectangular prism of base lengths 6 in and height 1 in is:

$Volume = 6^2 \times 1$

$Volume = 36$

Assume, he adds a cube of side length 4 in, the volume is:

$V = 4^3$

$V = 64$

The total volume would be:

$V =36 + 64$

$V =100$

The base length of the rectangular prism would be:

$Length =1+2+3+4$

$Length =10$

The volume of the rectangular prism would be:

$Volume = 10^2 \times 1$

$Volume = 100$

So, the pattern is:

Cubes                Volumes

1, 2, 3                    36

1, 2, 3,4                  100

Corry's conjecture is right, and the volume follows a pattern

Read more about conjectures at:

https://brainly.com/question/4125198