Question

A rectangular prism has a legth of 5 1/4 m, a width of 4m, and a height of 12 m.How many unit cubes with edge lengths of 1/4 m will it take to fill the prism? what is the volume of the prism?

Answer 1

Volume of a cube with edge lengths of 1/4m:

`\begin{gathered} V_(cube)=l^3 \\ \\ V_(cube)=((1)/(4)m)^3=(1^3)/(4^3)m^3=(1)/(64)m^3 \end{gathered}`

Volume of the rectangular prism:

`\begin{gathered} V=l\cdot w\cdot h \\ \\ V=5(1)/(4)m\cdot4m\cdot12m \\ \\ V=(21)/(4)m\cdot4m\cdot12m \\ \\ V=252m^3 \end{gathered}`

Divide the volume of the prism into the volume of the cubes:

`(252m^3)/((1)/(64)m^3)=252\cdot64=16128`

Then, to fill the prism it will take 16,128 cubes with edge length of 1/4 m