A rectangle prism has a length of 4 cm and a width of 1 1/2 cm and a height of 2 1/2 cm.how many unit cubes with edge lengths of 1/2 cm will it take to fill the prism? what is the volume of the prism?the prism can be filled with _ unit cubes that have edge lengths of 1/2 cmThe volume of the prism is _ cm3



Answer :

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