Answer:
A) 30 cubes.
B) 30 units³.
Step-by-step explanation:
A) 1. Calculate the volume of the rectangular prism, as following:
[tex]Vr=(lenght)(width)(height)[/tex]
2. You have that:
- The length is: [tex]1^{\frac{1}{2}}ft=1.5ft[/tex]
- The width is: [tex]1ft[/tex]
- The heigth is: [tex]2^{\frac{1}{2}}ft=2.5ft[/tex]
3. Substitute these values into the formula:
[tex]Vr=(1.5ft)(1ft)(2.5ft)=3.75ft^{3}[/tex]
4. The volume of one cube is:
[tex]Vc=side^{3}[/tex]
5. The length of one side is: [tex]\frac{1}{2}ft=0.5ft[/tex]
6. Substitute this value into the formula:
[tex]Vc=(0.5ft)^{3}=0.125ft^{3}[/tex]
7. The number of small cubes that can be packed in the rectangular prism is:
[tex]cubes=\frac{Vr}{Vc}\\cubes=\frac{3.75ft^{3}}{0.125ft^{3}}\\cubes=30[/tex]
B) 1. The length, the width and the height of the rectangular prism in term of units cubes is:
[tex]Length=\frac{1.5ft}{0.5ft}=3units[/tex]
[tex]Width=\frac{1ft}{0.5ft}=2units[/tex]
[tex]Heigth=\frac{2.5ft}{0.5ft}=5units[/tex]
2. Therefore, the volume of the rectagular prism in terms of the small cube and a unit cube is:
[tex]Vr=(3units)(2units)(5units)=30units^{3}[/tex]
