Question

EMERGENCY! How many cubes with side lengths of 1/2 cm does it take to fill the prism?

Answer 1

Answer:

  24 cubes

Step-by-step explanation:

You can figure this a couple of ways.

I usually find it easiest to figure in terms of the number of cubes each dimension represents. The vertical dimension (3/2 cm) is the length of 3 cubes; the front-back dimension (2 cm) is the length of 4 cubes, and the width (1 cm) is the length of 2 cubes.

The total number of cubes required is the product of the dimensions in cube-lengths: 3×4×2 = 24 cubes.

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Another way to figure this is to compute the prism volume in the given dimensions (cm³) and the cube volume in the same dimensions, then find the number of cube volumes in the prism volume.

  Prism volume = l×w×h = (2 cm)(1 cm)(3/2 cm) = 3 cm³

  Cube volume = (1/2 cm)³ = 1/8 cm³

Then the number of cubes that will fit in the prism is ...

  (3 cm³)/(1/8 cm³) = 3×8 = 24 . . . . cubes