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
