Answer:
48 cubic inches.
Explanation:
The volume of a rectangular prism is given by the formula:
Volume = length x width x height
Since the rectangular prism has a volume of 6 cubic inches, we can write:
6 = length x width x height
When the prism is dilated using a scale factor of 2, each of its dimensions (length, width, and height) is multiplied by 2. Therefore, the new dimensions of the prism are:
2 x length, 2 x width, and 2 x height
The volume of the dilated prism can be calculated as:
Volume of dilated prism = (2 x length) x (2 x width) x (2 x height)
= 2³ x length x width x height
= 8 x (length x width x height)
Since the original rectangular prism had a volume of 6 cubic inches, we know that:
length x width x height = 6
Substituting this value into the equation for the volume of the dilated prism, we get:
Volume of dilated prism = 8 x 6 = 48 cubic inches
Therefore, the volume of the dilated rectangular prism is 48 cubic inches.