Respuesta :
Volume of the cube with side 4p = 4p x 4p x 4p = 64p³
Volume of the cube with side 2q² = 2q² x 2q² x 2q² = 8q⁶
Total Volume = 64p³ + 8q⁶
Total Volume = (4p)³ + (2q²)³
Total Volume = (4p + 2q²)( ( 4p)² - (4p)(2q²) + (2q²)²)
Total Volume = (4p + 2q²)( 16p² - 8pq² + 4q⁴)
Answer: (4p + 2q²)( 16p² - 8pq² + 4q⁴)
Volume of the cube with side 2q² = 2q² x 2q² x 2q² = 8q⁶
Total Volume = 64p³ + 8q⁶
Total Volume = (4p)³ + (2q²)³
Total Volume = (4p + 2q²)( ( 4p)² - (4p)(2q²) + (2q²)²)
Total Volume = (4p + 2q²)( 16p² - 8pq² + 4q⁴)
Answer: (4p + 2q²)( 16p² - 8pq² + 4q⁴)
The total volume of the cubes in factored form is given by:[tex]\rm (4p+2q^2)(16p^2-8pq^2+4q^4)[/tex]
Given :
Cube with side length 4p is stacked on another cube with side length [tex]\rm 2q^2[/tex].
Solution :
We know that the volume of a cube is defined as the total number of cubic units occupied by the cube completely.
So the volume of cube is given by the formula:
[tex]\rm Volume = a\times a\times a[/tex]
Where, a is the side length of a cube.
Therefore the volume of cube of side length 4p is given by:
[tex]\rm V = 4p\times 4p \times 4p[/tex]
[tex]\rm V = 64p^3[/tex]
Now, the volume of cube of side length [tex]\rm 2q^2[/tex] is given by:
[tex]\rm V' = 2q^2\times 2q^2\times 2q^2[/tex]
[tex]\rm V' = 8q^6[/tex]
So the total volume = [tex]64p^3+8q^6[/tex]
[tex]\rm = (4p)^3+(2q^2)^3[/tex]
[tex]\rm = (4p+2q^2)((4p)^2-(4p)(2q^2)+(2q^2)^2)[/tex]
[tex]\rm =(4p+2q^2)(16p^2-8pq^2+4q^4)[/tex]
Therefore, the total volume of the cubes in factored form is given by:[tex]\rm (4p+2q^2)(16p^2-8pq^2+4q^4)[/tex]
For more information, refer the link given below
https://brainly.com/question/23409099
