Question

The dimensions of a rectangular prism are shown below:

Length: 1 and 1 over 3 feet
Width: 1 foot
Height: 2 and 1 over 3 feet
The lengths of the sides of a small cube are 1 over 3 foot each.

Part A: How many small cubes can be packed in the rectangular prism? Show your work. (5 points)

Part B: Use the answer obtained in part A to find the volume of the rectangular prism in terms of the small cube and a unit cube. (5 points)

Answer 1

please post it in the mathematics subject

Answer 2

Ok so in order to find part A, ` How many small cubes can be packed in the rectangular prism`
we would have to divide the mass of the cubes by the rectangular prism
that would tell us how many of `the value of a cube` could go into `the rectangular prism`
In other words how much times can \(\frac13ft\) go into the rectangular prism ( when Length: 1 and 1 over 3 feet~Width: 1 foot~Height: 2 and 1 over 3 feet)
(\(\frac13ft\) is how big each small cube is [since it's a cube every side has the same length])
So basically it's \(\frac13ft/*rectangular\ prism*\) or \(\frac13fr÷*rectangular\ prism*\)

Answer 3

So we have the dimensions:
\(L=1\frac13ft\\ W=1ft\\ H=2\frac13\)

Answer 4

So then we find the small cube's volume
\((\frac13)^3 = \frac{1}{27} ft^3\)
So then we basically combine them
~divide
\(\frac{\frac{28}{9}}{ \frac{1}{27}} = \frac{28}{9}*27 = 28*3\)
Which is basically \(\frac{28}{9} ÷ \frac{1}{27} = \frac{28}{9}*27 = 28*3\)
Which =?
that would be the number of small cubes that could fit inside the rectangular prism that has a length of \(1 \frac13ft\) a width of 1 foot, and height of \(2 \frac13\)
which would be your final answer