Answer:
9 inches long is the box.
Step-by-step explanation:
Volume of a cube is given by:
\(\text{Volume of a cube} = s^3\) where, s is the side of the cube
Volume of a box(V) is given by:
\(V = lwh\) .....[1]
where
l is the length , w is the width and h is the height of the box respectively.
As per the statement:
The number of one-inch cubes that will fit into a box that is 6 inches wide and one inch tall is 54.
Volume of one box = \(1^3 = 1\) in.
then;
Volume of 54 box = 54 inches.
It is also given:
w = 6 inches and h = 1 inch
Substitute in [1] we have;
\(54 = l \cdot 6 \cdot 1\)
⇒\(54 =6l\)
Divide both sides by 6 we get;
\(9 = l\)
or
\(l = 9 in.\)
therefore, 9 inches long is the box.
