Question

A cube with side length 5h^2 is stacked on another cube with side length 3k What is the total volume of the cubes in factored form?

Answer 1

In order to compute the combined volume of the cubes, we may simply add the individual volumes of the cube. The volume of a cube is equivalent to the cube of one of its sides. The volume of the first cube is (5h^2)^3 = 125h^6. The volume of the second cube is (3k)^3 = 27k^3. The total volume is: 125h^6 + 27k^3Hope this helps. Let me know if you need additional help!

Answer 2

`(5h^2+3k)(25h^4-15h^2k+9k^2)`

Explanation:

We have been given that a cube with side length 5h^2 is stacked on another cube with side length 3k.

Since we know that the volume of cube is
`a^3`, where a represents the length of each side of cube.

Since one cubes is stacked on another cube, so the total volumes of both cubes will be equal to the sum of volumes of both cubes.

`\text{Total volume of both cubes}=(5h^2)^3+(3k)^3`

Since the volume of both cubes is sum of cubes, so we will use formula:

`a^3+b^3=(a+b)(a^2-ab+b^2)`

So factoring the volumes of cubes using sum of cubes we will get,

`\text{Total volume of both cubes}=(5h^2+3k)((5h^2)^2-5h^2* 3k+(3k)^2)`

`\text{Total volume of both cubes}=(5h^2+3k)(25h^4-15h^2k+9k^2)`

Therefore, the total volume of both cubes in factored form will be:
`(5h^2+3k)(25h^4-15h^2k+9k^2)`