Question

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

Answer 1

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

So , The number of cubes to fill prism  

 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