The image shows a mathematical problem asking to find the total surface area of a cube that has one of its faces shaped into a rectangle with dimensions 10 cm by 50 cm.

Problem Explanation:

• A cube has six faces, and each face is a square.
• However, the problem mentions a face that is transformed into a rectangle of size 10 cm by 50 cm.
• The key to solving this problem is to determine if this face actually represents a different geometric shape or if it's referring to a part of the surface area of a cube.

However, given the context and standard math problems, it's likely asking for the total surface area of a cube with each side of the cube being equal to 10 cm.

Calculation:

If each side of the cube is 10 cm:

• Surface area of one face: $\text{Area} = 10 \times 10 = 100 \, \text{cm}^2$
• Total surface area of the cube: $6 \times 100 = 600 \, \text{cm}^2$

The options in the image also suggest this interpretation. Since the correct total surface area is 600 cm², the answer is the option that reflects this value.

Answer:

The total surface area of the cube is 600 cm².

Would you like more details or have any questions about the solution? Here are some related questions you might consider:

1. What is the formula for the surface area of a cube?
2. How do the dimensions of a cube relate to its volume?
3. How would you find the surface area of a rectangular prism instead of a cube?
4. What would happen to the surface area if the side length of the cube were doubled?
5. How is the surface area related to the length of the sides in three-dimensional figures?

Tip: When solving problems about geometric shapes, always check if the shape mentioned is altered or remains standard to avoid confusion.