#1**+1 **

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....

Melody
Jul 30, 2017

#5**0 **

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.

TheXSquaredFactor
Jul 31, 2017