Given the figure, we can deduce the following information:
Height=1/2 cm
Length=1/2 cm
Width= 1/6 cm
To determine the number of cubic blocks with a side length of 1/6 cm needed to fill the volume of the given prism, we first note that a cube has equal sides. So, the dimensions of the cube must be:
Height= 1/6 cm
Length=1/6 cm
Width=1/6 cm
Next, we get the volume of the cube by using the formula:
[tex]\begin{gathered} Volume\text{ of the cube}=(Height)(Length)(Width) \\ =(\frac{1}{6})(\frac{1}{6})(\frac{1}{6}) \\ Simplify \\ =\frac{1}{216}\text{ }cm^3\text{ } \end{gathered}[/tex]Then, we get the volume of the given prism using the same formula:
[tex]\begin{gathered} Volume\text{ of the given prism}=(He\imaginaryI ght)(Length)(W\imaginaryI dth) \\ =(\frac{1}{2})(\frac{1}{2})(\frac{1}{6}) \\ =\frac{1}{24}\text{ }cm^3\text{ } \end{gathered}[/tex]Now, we find the number cubic blocks by using the formula:
[tex]\begin{gathered} Number\text{ }of\text{ cubic blocks}=\frac{Volume\text{ of the given prism}}{Volume\text{ of the cube}} \\ =\frac{\frac{1}{24}}{\frac{1}{216}} \\ Simplify \\ =9 \end{gathered}[/tex]Therefore, the answer is 9.
