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How many 1/2-inch cubes would fit into a 96inch cubed rectanular prism?

Guest Jul 29, 2017
 #1
avatar+92917 
+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
 #2
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0

yes its 96in^3 

Guest Jul 30, 2017
 #4
avatar+92917 
0

I repeat:

 

Do you mean that the volume is   0.5cm^3 or do you mean that the side length of the cube is 0.5cm?

 

THEY ARE DIFFERENT!

 

BUT GUEST ANSWER  #3   IS CORRECT.

 

Thanks #3  :)

Melody  Jul 31, 2017
 #3
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+1

Just take the volume of rectangular prism divide by the volume of cube

Guest Jul 30, 2017
 #5
avatar+2143 
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

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