+118609 How many 1/2-inch cubes would fit into a 96inch cubed rectanular prism?
Do you mean that the volume is 0.5cm^3 or do you mean that the side length of the cube is 0.5cm?
Do you mean that the rectangular prism has a volume of 96cm^3? I guess that is what you mean....
+2441 I will end this controversy by considering both cases.
Case #1: If the side lengths are 1/2 inch.
To solve for this find the volume of the smaller cube. Finding the volume of a cube is actually simple. Just use the following formula.
\(V=s^3\)
Let V = volume of the cube
Let s = side length
| \(V=s^3\) | Plug in the side length for s, ½. |
| \(V=(\frac{1}{2})^3\) | "Distribute" the cube into both the numerator and denominator. |
| \(V=\frac{1^3}{2^3}\) | |
| \(V=\frac{1}{2*2*2}=\frac{1}{8}\) | Ok, the volume of the cube is 1/8in^3. |
To find how many of cubes with a volume of 1/8in^3 would fit in a 96in^3 rectangular prism, just divide them.
\(\frac{V_{rect.}}{V_{cube}}\)
Let's do that!
| \(\frac{V_{rect.}}{V_{cube}}\) | Just plug in the values are solve from there. |
| \(\frac{96}{\frac{1}{8}}\) | We will use a fraction rule that states that \(\frac{a}{\frac{b}{c}}=\frac{a*c}{b}\) |
| \(\frac{96}{\frac{1}{8}}=\frac{96*8}{1}=768\) | |
Therefore, \(768\) cubes with a length of 1/2in can fit in a rectangular prism with a volume of 96in^3.
Case #2: If the cube has a volume of 1/2in^3
We already know the volume of both cubes, so divide the rectangular prism's volume from the cube's volume:
| \(\frac{96}{\frac{1}{2}}\) | I will utilize a fraction rule that states that \(\frac{a}{\frac{b}{c}}=\frac{a*c}{b}\) |
| \(\frac{96}{\frac{1}{2}}=\frac{96*2}{1}=192\) | |
In this scenario, \(192\) cubes of a volume of 1/2in^3 can fit in a rectangular prism with a volume of 96in^3.
