Mathematics Middle School

Surface Area
Part A
What is the area of each face of cube A?
Part B
How can you calculate the surface area of cube A? What is the surface area of cube A?
Part C
What is the area of each face of cube B?
Part D
How is the area of each face of cube B related to the area of each face of cube A?
Part E
What is the surface area of cube B?

Answers

Answer 1
Part A: The area of each face of cube A is equal since all faces of a cube are identical. Therefore, the area of each face of cube A is given by the formula A = s^2, where s is the length of any side of the cube.
Part B: To calculate the surface area of cube A, we need to find the area of all six faces and add them together. Since all faces of a cube are identical, we can use the formula A = s^2 to find the area of one face and then multiply it by 6 to get the total surface area. Therefore, the surface area of cube A is given by the formula SA = 6s^2.
Part C: The area of each face of cube B is also equal since all faces of a cube are identical. Therefore, the area of each face of cube B is given by the formula A = s^2, where s is the length of any side of the cube.
Part D: The area of each face of cube B is related to the area of each face of cube A because both cubes have the same shape and size. Therefore, the area of each face of cube B is equal to the area of each face of cube A.
Part E: The surface area of cube B can be calculated using the same formula as cube A, which is SA = 6s^2, where s is the length of any side of the cube. Since cube B has the same shape and size as cube A, the surface area of cube B is also equal to 6 times the area of one face, which is given by the formula A = s^2. Therefore, the surface area of cube B is also equal to SA = 6s^2.
Answer 2
Part A:
Each face of cube A has the same area since it's a cube. To find the area of each face, you can use the formula for the area of a square: side length squared.

Part B:
To calculate the surface area of cube A, you can multiply the area of one face by the number of faces. Since a cube has 6 faces, the surface area of cube A is 6 times the area of one face.

Part C:
Cube B is also a cube, so each face has the same area as the faces of cube A.

Part D:
The area of each face of cube B is equal to the area of each face of cube A since they are both cubes.

Part E:
The surface area of cube B is also 6 times the area of one face, just like cube A.

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