Question

From all sides of the given cube, a smaller cube(shaded) is removed, what will be the increase in surface area of the cube if all the shaded faces are identical? ​

Answer 1

Answer: Look! When you remove that cube, you’re taking away 3 faces, but you’re also exposing 3 more previously unexposed faces! And those newly exposed faces have the exact same areas as the faces you took away. So the surface area, amazingly enough, remains the same.

You’ve got a 3\times 3\times 3 cube there. The original area of each face was 9, and of course, all cubes have 6 faces. So the original cube had a surface area of 54.

When you remove the corner piece, you’ve got 54 – 3 + 3 = 54.

Step-by-step explanation: