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To solve this problem, we are asked to find the curved surface area of the frustum. A frustum is formed by removing the top portion of a cone (a smaller cone) from a larger cone.

### Information given:
- Curved surface area of the large cone = \( 50 \, \text{m}^2 \)
- Curved surface area of the small cone = \( 5 \, \text{m}^2 \)

### Key Concept:
The curved surface area of a frustum is the difference between the curved surface area of the larger cone and the smaller cone (which was removed from the top).

### Formula:
\[
\text{Curved surface area of frustum} = \text{Curved surface area of large cone} - \text{Curved surface area of small cone}
\]

### Substituting values:
\[
\text{Curved surface area of frustum} = 50 \, \text{m}^2 - 5 \, \text{m}^2 = 45 \, \text{m}^2
\]

Thus, the curved surface area of the frustum is \( 45 \, \text{m}^2 \).

Would you like more details or explanations on this problem?

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### Related Questions:
1. How is the volume of a frustum calculated if the heights are provided?
2. What is the lateral surface area of a cone, and how is it calculated?
3. How would the solution change if the cones weren't similar?
4. What other real-world applications involve calculating the surface area of a frustum?
5. How does the surface area formula change if the frustum has slant height provided?

**Tip:** Always verify if the shapes are geometrically similar when working with frustums, as this greatly simplifies calculations.

A large cone is split horizontally to form a similar, smaller cone and a frustum. The curved surface area of the large cone is 50 m². The curved surface area of the small cone is 5 m². Work out the curved surface area of the frustum.

Learn how to calculate the curved surface area of a frustum formed by splitting a cone. In this example, the curved surface areas of the larger and smaller cones are 50 m² and 5 m², respectively. By subtracting the smaller area from the larger one, we find the curved surface area of the frustum to be 45 m².

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