Question

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

Answer 1

The volume of the rectangular prism is 1 cubic inch, calculated by multiplying its dimensions: 3 inches by 1 inch by 1/3 inch. The student's claim that 108 cubes are needed is incorrect; only 27 are required.

Step-by-step explanation:

To calculate the volume of a rectangular prism, you multiply the length by the width by the height. In this case, the dimensions of the prism are 3 inches by 1 inch by 1/3 inch. Accordingly, the volume of the rectangular prism can be calculated as follows:

Volume = length × width × height

Volume = 3 in × 1 in × 1/3 in = 1 in³

Therefore, the correct volume of the rectangular prism is 1 cubic inch, which means the answer provided by Diego regarding requiring 108 cubes each with a volume of 1/27 cubic inches (since the edge length is 1/3 inch, and cube volume is edge length cubed) to fill the rectangular prism is incorrect. The actual number of these small cubes required to fill the prism would be 27, which is 1 in³ / (1/3 in)^3.

As such, the correct answer for the volume of the rectangular prism is 1 cubic inch.

Answer 2

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,

• Volume of a cube = a³
• where a represents the edge length

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)