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A rectangular prism has a volume of 6 cubic inches. It is dilated using a scale factor of 2, what is the volume of the dilated rectangular prism?

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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.

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