Need some help with this problem. If you have a cube that is made up of 27 individual cubes. The entire cube has 3 length, 3 width, and 3 height if you take one cube away from each of the 8 vertices, what is the surface area of the cube? thanks
To find the surface area of the cube after removing one cube from each of the 8 vertices, we need to calculate the surface area of the original cube and subtract the surface area of the 8 removed cubes.
Let's break down the steps to get the final answer:
Step 1: Calculate the surface area of the original cube.
The surface area of a cube is given by the formula: 6 * side^2.
Since the original cube has a side length of 3, the formula becomes:
Surface Area of the original cube = 6 * 3^2 = 6 * 9 = 54.
Step 2: Calculate the surface area of one removed cube.
Each cube has 6 equal faces, and since the original cube has a side length of 3, the removed cube also has a side length of 3.
Therefore, the surface area of one removed cube = 6 * 3^2 = 6 * 9 = 54.
Step 3: Calculate the surface area of all 8 removed cubes.
Since there are 8 removed cubes, the total surface area of the removed cubes is 8 * 54 = 432.
Step 4: Calculate the final surface area of the modified cube.
The final surface area is obtained by subtracting the surface area of the removed cubes from the surface area of the original cube.
Final Surface Area = Surface Area of original cube - Surface Area of removed cubes
Final Surface Area = 54 - 432 = -378.
Therefore, the surface area of the modified cube after removing one cube from each of the 8 vertices is -378 square units.