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 [tex]4\frac{1}{4}[/tex] in.
The prism is filled with cubes that have edge lengths of [tex]\frac{1}{4}[/tex] 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 [tex]4\frac{1}{4}=\frac{17}{4}[/tex] in.
Volume of rectangular prism is [tex]V=L\times B\times H[/tex]
[tex]V=12\times 5\times \frac{17}{4}[/tex]
[tex]V=255 in^3[/tex]
A cube has length of [tex]\frac{1}{4}[/tex] in.
Volume of cube is [tex]V=L^3[/tex]
[tex]V=\frac{1}{4}^3[/tex]
[tex]V=\frac{1}{64}in^3[/tex]
Cubes are needed to fill the rectangular prism is
[tex]=\frac{\text{Volume of rectangular prism}}{\text{Volume of cubes}}[/tex]
[tex]=\frac{255}{\frac{1}{64}}[/tex]
[tex]=255\times 64[/tex]
[tex]=16320[/tex]
Therefore, 16320 cubes are needed to fill the rectangular prism.
Answer:
Step-by-step explanation:
The volume of a rectangular prism is
[tex]V=l \times h \times w[/tex]
Where [tex]l[/tex] is the length, [tex]h[/tex] is the height and [tex]w[/tex] is the width.
In this case, we have
[tex]l=12in\\h=414in\\w=5in[/tex]
Replacing this values we can find the volume
[tex]V=12in (5in)(414in)=24,840 in^{3}[/tex]
Now, the cubes needed have edge lengths of 14 in, that means their volume is
[tex]V_{cube} = l^{3} =(14in)^{3}=2,744 in^{3}[/tex]
To know how many cubes are needed, we just need to divide
[tex]n=\frac{24,840}{2,744} \approx 9[/tex]
Therefore, there are needed 9 cubes.
