Answer:
Volume of the rectangular prism is [tex]11\frac{1}{4}[/tex] cubic feet.
The number of small cubes required is 90.
Step-by-step explanation:
The rectangular prism has a length of [tex]2\frac{1}{2}[/tex] feet, a width of 3 feet, and a height of [tex]1\frac{1}{2}[/tex] feet.
Now, the volume of the rectangular prism will be [tex](2\frac{1}{2} \times 3 \times 1\frac{1}{2}) = (\frac{5}{2} \times 3 \times \frac{3}{2}) = \frac{45}{4}[/tex] cubic feet i.e. [tex]11\frac{1}{4}[/tex] cubic feet. (Answer)
Now, the volume of the small unit cubes of side lengths of [tex]\frac{1}{2}[/tex] feet will be [tex](\frac{1}{2})^{3} = \frac{1}{8}[/tex] cubic feet.
So, the number of small cubes required to fill the large cube will be [tex](\frac{45}{4} \div \frac{1}{8}) = 90[/tex]. (Answer)
