Your teacher will give you cubes that have edge lengths of inch.

1. Here is a drawing of a cube with edge lengths of 1 inch.

   1. How many cubes with edge lengths of inch are needed to fill this cube?

      

   2. What is the volume, in cubic inches, of a cube with edge lengths of inch? Explain or show your reasoning.

2. Four cubes are piled in a single stack to make a prism. Each cube has an edge length of inch. Sketch the prism, and find its volume in cubic inches.

3. Use cubes with an edge length of inch to build prisms with the lengths, widths, and heights shown in the table.

   For each prism, record in the table how many -inch cubes can be packed into the prism and the volume of the prism.

   prism length (in)	prism width (in)	prism height (in)	number of -inch cubes in prism	volume of prism (in3)
   1	1
   2	1
   2	2	1
   4	2
   5	4	2
   5	4

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

   

   

   1. Explain or show how this is true.

   2. What is the volume, in cubic inches, of the rectangular prism? Explain or show your reasoning.

2. Lin and Noah are packing small cubes into a larger cube with an edge length of inches. Lin is using cubes with an edge length of inch, and Noah is using cubes with an edge length of inch.

   1. Who would need more cubes to fill the -inch cube? Be prepared to explain your reasoning.

   2. If Lin and Noah each use their small cubes to find the volume of the larger -inch cube in cubic inches, will they get the same answer? Explain or show your reasoning.

   

A nature center has a fish tank in the shape of a rectangular prism.
The tank is 10 feet long, feet wide, and 6 feet tall.

1. What is the volume of the tank in cubic feet? Show your reasoning.

   

2. One day, a caretaker filled of the tank with water. What was the volume of the water in the tank, in cubic feet? What was the height of the water in the tank? Show your reasoning.