Answer :
518 cubes are needed to fill the right rectangular prism without gaps or overlaps.
What is right rectangular prism?
"It is a prism whose all faces are rectangles."
What is the volume of rectangular prism?
The volume of a rectangular prism with length l, width w and height h is,
V = l × w × h
What is the volume of cube?
The volume of a cube having side length 'a' is given by,
[tex]V=a^3[/tex]
For given example,
The dimensions of a right rectangular prism are:
length : [tex]l=2\frac{1}{6}[/tex]
⇒ [tex]l=2.17[/tex] in.
width: [tex]w=1\frac{1}{6}[/tex]
⇒ [tex]w= 1.17[/tex] in.
height : h = 1 in.
So, the volume of a right rectangular prism would be,
⇒ V = l × w × h
⇒ V = 2.17 × 1.17 × 1
⇒ V = 2.5389 cu. in .
Now, the side lengths of a cube : [tex]a=\frac{1}{6}[/tex]
⇒ [tex]a=0.17[/tex]
So, the volume of a cube would be,
⇒ [tex]V=a^3[/tex]
⇒ V = (0.17)^3
⇒ V = 0.0049
Let, 'n' cubes are needed to fill the right rectangular prism without gaps or overlaps.
volume of a right rectangular prism = n × volume of a cube
⇒ 2.5389 = n × 0.0049
⇒ 2.5389/0.0049 = n
⇒ n = 518.14
⇒ n ≈ 518
Therefore, 518 cubes are needed to fill the right rectangular prism without gaps or overlaps
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