Question

a sealed rectangular container has a length 15p meters, width 12p meters, and hight 6p meter. how many cubes each of lenght 2p meters can be packed. how many cubes each of length 2p meters can be packedinto rectangular container?

Answer 1

What we need to calculate first is the volume of the container. Remember that the volume of a rectangular prism can be calculate like this:

$volume = L * W * H$
L = 15p
W = 12p
H = 6p

So volume would be:

$V_{rect} = 15p * 12p * 6p$
which equals
$V_{rect} = 1080p^{3}$ meters³

Now we want to know how many cubes with a length of 2p meters can be packed into this space. To know that, we have to calculate the volume of a single cube. The volume equation for a cube is this:

$volume = L^{3}$ which can also be written as
$volume = L * L * L$ since cubes have equal lengths
L = 2p

So let's calculate that volume!

$V = 2p * 2p * 2p$
$V _{cube} = 8p^{3}$ meters³

$V_{rect} = 1080p^{3}$
$V_{cube} = 8p ^{3}$

If we want to know how many cubes fit into the rectangular prism, we just have to divide $V_{rect}$ by $V_{cube}$:

$number of cubes = \frac{V_{rect} }{ V_{cube} }$
$number of cubes = \frac{1080p^{3} }{ 8 p^{3} }$

The p³ will cancel out leaving us with this:

Number of Cubes = 135 cubes will fit into the prism