Bates Bush
02/12/2024 · Primary School

What is a cross-section of a solid, and how can it be used to understand the volume of the solid?

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A **cross-section** of a solid is the shape formed by slicing the solid with a plane. To understand the volume of a solid, you can: 1. **Identify Cross-Sectional Shapes:** Examine how the solid looks when sliced at different points. 2. **Use Integration:** Calculate the area of each cross-section and add them up (integrate) to find the total volume. 3. **Apply Cavalieri’s Principle:** If two solids have the same height and cross-sectional areas at every level, they have the same volume. This method helps in determining the volume of complex shapes by breaking them down into simpler, two-dimensional parts.

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