Question

A rectangular prism has a length of 12 in., a width of 5 in., and a height of 414 in.

Answer 1

Answer:

There are needed 9 cubes.

Step-by-step explanation:

The volume of a rectangular prism is

$V=l \times h \times w$

Where $l$ is the length, $h$ is the height and $w$ is the width.

In this case, we have

$l=12in\\h=414in\\w=5in$

Replacing this values we can find the volume

$V=12in (5in)(414in)=24,840 in^{3}$

Now, the cubes needed have edge lengths of 14 in, that means their volume is

$V_{cube} = l^{3} =(14in)^{3}=2,744 in^{3}$

To know how many cubes are needed, we just need to divide

$n=\frac{24,840}{2,744} \approx 9$

Therefore, there are needed 9 cubes.

Answer 2

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.