The volume of the dilated cube is [tex]9375 \ {cm}^{3}[/tex]
Explanation:
The volume of the cube is [tex]75 \ {cm}^{3}[/tex]
It is given that the cube is dilated by a factor of 5.
We need to determine the volume of the dilated cube.
Since, we know that the dilation is a transformation that changes the size of the image but not the shape.
Since, it is given that the volume of the cube is dilated by a factor of 5, the length of the image will be 5 times greater, the width of the image will be 5 times greater and the height of the image will be times greater than the original image.
Thus, the volume of the dilated cube is given by,
[tex]Volume = (5\times5\times5)(volume \ of \ the \ original \ cube)[/tex]
[tex]= (5\times5\times5)(75)[/tex]
[tex]=(125)(75)[/tex]
[tex]=9375 \ {cm}^{3}[/tex]
Thus, the volume of the dilated cube is [tex]9375 \ {cm}^{3}[/tex]
