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Anna [14]
3 years ago
6

How many cubes with side lengths of 1/3 cm does it take to fill the prism?

Mathematics
1 answer:
user100 [1]3 years ago
8 0

Answer:

The number of cubes that fill the prism is 24

Step-by-step explanation:

Given as :

The length of cube (l) = \frac{1}{3} cm

The length of prism (L) = 1 cm

The width of prism (w) = 2 \frac{2}{3} = \frac{8}{3} cm

The height of prism (h) = \frac{2}{3} cm

Let the number of cubes that fill the prism = x

Now, Volume of cube with length (l) = l³   cm³

Or,  Volume of cube with length (l) = (\frac{1}{3})^{3}  cm³

Or,  Volume of cube with length (l) = (\frac{1}{27})  cm³

Again , Volume of prism  = \frac{1}{2}\times Length \times width \times height

Or, Volume of prism = \frac{1}{2}\times 1 \times \frac{8}{3} \times \frac{2}{3}

Or, Volume of prism = (\frac{8}{9})  cm³

<u>So , The number of cubes to fill prism  </u>

 The number of cubes × Volume of cube = Volume of prism

Or, x × (\frac{1}{27})  cm³ = (\frac{8}{9})  cm³

or   x = \frac{8\times 27}{9} = 24

Hence The number of cubes which fill the prism is 24  Answer

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