A rectangular prism has a length of 9 in., a width of 4 in., and a height of 1 1 2 in. The prism is filled with cubes that have edge lengths of 1 2 in. How many cubes are needed to fill the rectangular prism? Enter your answer in the box. To fill the rectangular prism, cubes are needed.

"A rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges."

What is a cube?

"A cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. It has 6 faces, 12 edges, and 8 vertices."

Given, the length of the prism is 9 inches.

The width of the prism is 4 inches.

The height of the prism is [tex]1\frac{1}{2}[/tex] inches.

Therefore, the volume of the rectangular prism is

= length × width × height

= 9 × 4 × 1.5 (inches)³

= 54 (inches)³

Again, the edge length of the cube is [tex]\frac{1}{2}[/tex] inches.

Therefore, the volume of the cube is

= (edge length)³

= (0.5)³ (inches)³

= 0.125 (inches)³

Now, the number of cubes that can be fitted inside the rectangular prism is = (volume of the rectangular prism) / (volume of the cube)

= [tex]\frac{54}{0.125}[/tex]

= 432

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