Recall the formula for the volume of a cube and use the cube root to find the edge length of the box.
0.3 centimeters
Practice makes perfect
We want to find the difference between the height of the puzzle cube and the top of the box when we place the cube in the box. To do so, we will find the length of one edge of the box first. Let s be the edge length of the box.
Because the box is a cube and its volume is 216 cm^3, we will use the formula for the volume of a cube to find the edge length.
V=s^3
In this formula, V is the volume of a cube and s is the edge length. Now, we will substitute 216 for V in the formula and solve it for s. Notice that in this equation s is cubed so we need to take the cube root to find its value. Let's do it!
We found that the edge length of the box is 6 centimeters.
Now, we will find the difference between their heights by subtracting the edge length of the puzzle cube from edge length of the box.
6- 5.7=0.3
The difference between the height of the puzzle cube and the top of the box is 0.3 centimeters.
