Volume of a Rectangular Prism
The dimensions of a rectangular prism are:
L = 4 cm
W = 1 1/2 cm
H = 2 1/2 cm
We'll convert the mixed fractions to improper fractions:
[tex]W=1\frac{1}{2}=1+\frac{1}{2}=\frac{3}{2}[/tex][tex]H=2\frac{1}{2}=2+\frac{1}{2}=\frac{5}{2}[/tex]The volume of the prism is:
[tex]V=L\cdot W\cdot H=4\cdot\frac{3}{2}\cdot\frac{5}{2}=15\operatorname{cm}^3[/tex]The unit cube has a length of 1/2 cm. The volume of each cube is
[tex]V^{\prime}=(\frac{1}{2})^3=\frac{1}{8}cm^3[/tex]To find the number of unit cubes that fill the prism, we divide both volumes as follows:
[tex]\frac{15}{\frac{1}{8}}=15\cdot8=120[/tex]The prism can be filled with 120 unit cubes
The volume of the prism is 15 cm3