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
