Answer:
48 cubes
Explanation:
Given
Cube
[tex]Side\ Length = \frac{1}{3}cm[/tex]
Prism [Missing from the question]
[tex]Length = 1cm[/tex]
[tex]Width= 2\frac{2}{3}cm[/tex]
[tex]Height = \frac{2}{3}cm[/tex]
Required
Determine the number of cubes the prism can take
Volume is calculated as:
[tex]V = Length * Width * Height[/tex]
First, calculate the volume of the cube
[tex]V_1 = \frac{1}{3} * \frac{1}{3} * \frac{1}{3} cm^3[/tex]
[tex]V_1 = \frac{1}{27} cm^3[/tex]
Next, calculate the volume of the prism
[tex]V_2 = 1 * 2\frac{2}{3} * \frac{2}{3}\ cm^3[/tex]
Convert to improper fraction
[tex]V_2 = 1 * \frac{8}{3} * \frac{2}{3}\ cm^3[/tex]
[tex]V_2 = \frac{16}{9}\ cm^3[/tex]
Divide V2 by V1 to get the number of cubes
[tex]Number = \frac{V_2}{V_1}[/tex]
[tex]Number = \frac{16}{9}/\frac{1}{27}[/tex]
[tex]Number = \frac{16}{9}*\frac{27}{1}[/tex]
[tex]Number = \frac{16*27}{9*1}[/tex]
[tex]Number = \frac{432}{9}[/tex]
[tex]Number = 48[/tex]
Hence, 48 cubes will fill the prism
