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

Jul 29, 2017

#1
+95230
+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....

Jul 30, 2017
#2
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yes its 96in^3

Guest Jul 30, 2017
#4
+95230
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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
+1

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

Jul 30, 2017
#5
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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.

Jul 31, 2017