First from the information we have, we see that the volume of the cube is 27cm3. So what are the dimensions of its length, width and height? This information will help us to determine the dimensions of the square pyramid.
Volume of a cube is found from the formula V = a3
Where V is volume, and a is the length of one side.
We expand this equation to be:
V= a * a * a
Since all sides of a cube are equal, then this equation will be:
27 = 3 * 3 * 3
Now we know the length width and height of the cube.
Volume of a square pyramid is given by the formula V =1/3ah
Where V is the volume, a is the area of the base of the pyramid, h is the height of the pyramid.
Since it fits perfectly into the cube, then its dimensions are the same as the cube, so:
Area of the base is Length * Width so:
a = 3 * 3 = 9
and height:
h = 3
Now therefore:
V = 1/3 * 9 * 3
V = 1/3 * 27
V = 27/3
V = 9 cm3