hink About the Process A right rectangular prism has length
​, width
​, and height
. You use cubes with fractional edge length
to find the volume. How many cubes are there for each of the​ length, width, and height of the​ prism? Find the volume.
How many cubes are there for each of the​ length, width, and height of the​ prism?
The length has
nothing ​cubes, the width has
nothing ​cubes, and the height has
nothing cubes.

Answer:

The length has 3 cubes

The width has 7 cubes

The height has 5 cubes

Step-by-step explanation:

Given

[tex]Length = 1\frac{1}{2}yd[/tex]

[tex]Width = 3\frac{1}{2}yd[/tex]

[tex]Height = 2\frac{1}{2}yd[/tex]

[tex]l = \frac{1}{2}yd[/tex] --- edge length

Required

Determine the number of cubes in each dimension

To do this, we divide the dimension by the edge length

For the length, we have:

[tex]n_{Length} = \frac{Length}{l}[/tex]

[tex]n_{Length} = \frac{1\frac{1}{2}}{\frac{1}{2}}[/tex]

Express as:

[tex]n_{Length} = 1\frac{1}{2} \div \frac{1}{2}[/tex]

Change to product

[tex]n_{Length} = 1\frac{1}{2} * \frac{2}{1}[/tex]

[tex]n_{Length} = 1\frac{1}{2} * 2[/tex]

[tex]n_{Length} = 3[/tex]

3 cubes in the length

For the width, we have:

[tex]n_{Width} = \frac{Width}{l}[/tex]

[tex]n_{Width} = \frac{3\frac{1}{2}}{\frac{1}{2}}[/tex]

Express as:

[tex]n_{Width} = 3\frac{1}{2} \div \frac{1}{2}[/tex]

Change to product

[tex]n_{Width} = 3\frac{1}{2} * \frac{2}{1}[/tex]

[tex]n_{Width} = 3\frac{1}{2} * 2[/tex]

[tex]n_{Width} = 7[/tex]

7 cubes in the width

For the height, we have:

[tex]n_{Height} = \frac{Height}{l}[/tex]

[tex]n_{Height} = \frac{2\frac{1}{2}}{\frac{1}{2}}[/tex]

Express as:

[tex]n_{Height} = 2\frac{1}{2} \div \frac{1}{2}[/tex]

Change to product

[tex]n_{Height} = 2\frac{1}{2} * \frac{2}{1}[/tex]

[tex]n_{Height} = 2\frac{1}{2} * 2[/tex]

[tex]n_{Height} = 5[/tex]

7 cubes in the height

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