Diego correctly points out that 108 cubes with an edge length of 1/3 inch are needed to fill a rectangular prism that is 3 inches by 1 inch by 1/3 inch.

What is the volume, in cubic inches, of the rectangular prism? Show your reasoning.

A. 64 cubic inches

B. 4 in

C. 4 cubic inches

Option C) 4 cubic inches is the volume of the rectangular prism.

Step-by-step explanation:

It is given that, 108 cubes with an edge length of 1/3 inch are needed to fill a rectangular prism.

Therefore, the volume of the rectangular prism is equal to the volume of the 108 cubes needed to fill that rectangular prism.

So, we need to find out the volume of those 108 cubes in order to find the volume of the rectangular prism.

The formula for finding the volume of a cube is given by,

We know that, the edge length is 1/3 inch.

⇒ a = 1/3

Volume of a cube = (1/3)³

⇒ 1/3 × 1/3 × 1/3

⇒ 1/27 cubic inches

To find the volume of 108 cubes :

⇒ 108 × volume of one cube

⇒ 108 × 1/27

⇒ 4 cubic inches.

∴ The volume of 108 cubes is the volume of rectangular prism which is 4 cubic inches (option C)