Answer:
[tex]\displaystyle 1\frac{1}{8}[/tex] ft³
Step-by-step explanation:
First, the box is one foot tall. In other words, it has a height of 1 foot. Since one cube is equal to [tex]\frac{1}{4}[/tex] ft, and the box is four cubes tall,
[tex]\frac{1}{4}[/tex] ft + [tex]\frac{1}{4}[/tex] ft + [tex]\frac{1}{4}[/tex] ft + [tex]\frac{1}{4}[/tex] ft = 1 foot
Now, it has a width of [tex]\frac{3}{4}[/tex] ft because, as stated above, one cube is equal to [tex]\frac{1}{4}[/tex] ft. The box has three cubes making up the width.
[tex]\frac{1}{4}[/tex] ft + [tex]\frac{1}{4}[/tex] ft + [tex]\frac{1}{4}[/tex] ft = [tex]\frac{3}{4}[/tex] ft
Next, it has a length of [tex]\frac{3}{2}[/tex] ft because, as stated twice above, one cube is equal to [tex]\frac{1}{4}[/tex] ft. The box has six cubes making up the length.
[tex]\frac{1}{4}[/tex] ft + [tex]\frac{1}{4}[/tex] ft + [tex]\frac{1}{4}[/tex] ft + [tex]\frac{1}{4}[/tex] ft + [tex]\frac{1}{4}[/tex] ft + [tex]\frac{1}{4}[/tex] ft = [tex]\frac{6}{4}[/tex] ft = [tex]\frac{3}{2}[/tex] ft
Lastly, we will solve for the full volume of the box.
V = L * W * H
V = [tex]\frac{3}{2}[/tex] ft * [tex]\frac{3}{4}[/tex] ft * 1 ft
V = [tex]\displaystyle \frac{3*3*1}{2*4}[/tex] ft³
V = [tex]\displaystyle \frac{9}{8}[/tex] ft³
V = 1 [tex]\displaystyle \frac{1}{8}[/tex] ft³
