Laney builds a tower with wooden Cubes. The bottom Cubes edges are 8 centimeters long. The middle cubes edges are 2 centimeters shorter than the bottom cube. The top cube's edges are 2 centimeters shorter than the middle cube. What is the total volume Of the cubes in the tower?'
The cubes have sides of 8,6,4 so the total volume is
8^3 + 6^3 + 4^3 = 512+216+64 = ___
792
To find the total volume of the cubes in the tower, we need to calculate the volume of each cube and then add them together.
Let's assume the length of the edges of the bottom cube is x centimeters.
Given that the middle cube's edges are 2 centimeters shorter than the bottom cube, the length of the edges of the middle cube would be (x - 2) centimeters.
Similarly, the length of the edges of the top cube, which is 2 centimeters shorter than the middle cube, would be ((x - 2) - 2) centimeters, which simplifies to (x - 4) centimeters.
The formula to calculate the volume of a cube is V = s^3, where V is the volume and s is the length of one edge.
Therefore, the volume of the bottom cube would be x^3 cubic centimeters.
The volume of the middle cube would be (x - 2)^3 cubic centimeters.
And the volume of the top cube would be (x - 4)^3 cubic centimeters.
To find the total volume, we need to add the volumes of all the cubes:
Total Volume = Volume of Bottom Cube + Volume of Middle Cube + Volume of Top Cube
Total Volume = x^3 + (x - 2)^3 + (x - 4)^3
Simplifying the equation further, we can find the value of x and calculate the total volume.
To find the total volume of the cubes in the tower, we need to find the volume of each cube and add them together.
Let's first find the volume of the bottom cube. The edges of the bottom cube are 8 centimeters long, so the volume of the bottom cube is calculated using the formula: volume = edge length^3.
Volume of the bottom cube = 8^3 = 512 cm^3.
Now, let's find the volume of the middle cube. The edges of the middle cube are 2 centimeters shorter than the bottom cube. So the edge length of the middle cube is 8 - 2 = 6 centimeters.
Volume of the middle cube = 6^3 = 216 cm^3.
Lastly, let's find the volume of the top cube. The edges of the top cube are 2 centimeters shorter than the middle cube. So the edge length of the top cube is 6 - 2 = 4 centimeters.
Volume of the top cube = 4^3 = 64 cm^3.
Now, let's add the volumes of all three cubes to find the total volume of the tower:
Total volume = Volume of bottom cube + Volume of middle cube + Volume of top cube
= 512 cm^3 + 216 cm^3 + 64 cm^3
= 792 cm^3.
Therefore, the total volume of the cubes in the tower is 792 cubic centimeters.