Question

A cube with a volume of 75 cmis dilated by a factor of 5.

What is the volume of the dilated cube?

Answer 1

The volume of the dilated cube is
`9375 \ {cm}^(3)`

Step-by-step explanation:

The volume of the cube is
`75 \ {cm}^(3)`

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,

`Volume = (5*5*5)(volume \ of \ the \ original \ cube)`

`= (5*5*5)(75)`

`=(125)(75)`

`=9375 \ {cm}^(3)`

Thus, the volume of the dilated cube is
`9375 \ {cm}^(3)`