Question

A rectangular prism has a length of 4 in., a width of 2 in., and a height of 2 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?



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Answer 1

160

Explanation:

Each cube is 1/2 inch, so there will be 2 cubes in each 1 inch of length. The dimensions of the prism in terms of the number of cubes are ...

length: 4 in ⇒ 4×2 = 8 cubes

width: 2 in ⇒ 2×2 = 4 cubes

height: 2 1/2 in ⇒ (2 1/2)×2 = 5 cubes

Then the number of cubes required to fill the prism is ...

8 × 4 × 5 = 160 . . . . cubes

The volume of the prism is equivalent to that of 160 1/2-inch cubes.