Answer:
16320 cubes are needed to fill the rectangular prism.
Step-by-step explanation:
Given : A rectangular prism has a length of 12 in., a width of 5 in., and a height of \(4\frac{1}{4}\) in.
The prism is filled with cubes that have edge lengths of \(\frac{1}{4}\) in.
To find : How many cubes are needed to fill the rectangular prism?
Solution :
A rectangular prism has
Length of 12 in.
Width of 5 in.
Height of \(4\frac{1}{4}=\frac{17}{4}\) in.
Volume of rectangular prism is \(V=L\times B\times H\)
\(V=12\times 5\times \frac{17}{4}\)
\(V=255 in^3\)
A cube has length of \(\frac{1}{4}\) in.
Volume of cube is \(V=L^3\)
\(V=\frac{1}{4}^3\)
\(V=\frac{1}{64}in^3\)
Cubes are needed to fill the rectangular prism is
\(=\frac{\text{Volume of rectangular prism}}{\text{Volume of cubes}}\)
\(=\frac{255}{\frac{1}{64}}\)
\(=255\times 64\)
\(=16320\)
Therefore, 16320 cubes are needed to fill the rectangular prism.
