Question

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

Answer 1

The volume of the dilated cube is $9375 \ {cm}^{3}$

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,

$Volume = (5\times5\times5)(volume \ of \ the \ original \ cube)$

            $= (5\times5\times5)(75)$

            $=(125)(75)$

            $=9375 \ {cm}^{3}$

Thus, the volume of the dilated cube is $9375 \ {cm}^{3}$