Cross-Sections and Scale Factors

Cross-Sections

Different solids can be cut at different angles to create different cross sections. Remember that a cross section is a flat shape, not a solid object or a line. The image shows some possible cross-sections of a cylinder.

Exploring Scale Factors

For each square, the side lengths are 2, 3 and 4 times bigger than the original 1-inch square

• The 2-inch square fits 4 squares

• The 3-inch square fits 9 squares

• The 4-inch square fits 16 squares

Instead of being 2, 3, or 4 times bigger than the original area, the areas are 4, 9, and 16 times bigger.

The area scaled up by the original scale factor squared.

Exploring Scale Factors

For each cube, the side lengths are 2, 3 and 4 times bigger than the original 1-inch cube

• The 2-inch cube needs 8 cubes

• The 3-inch square needs 27 cubes

• The 4-inch square needs 64 cubes

Instead of being 2, 3, or 4 times bigger than the original area, the volumes are 8, 27, and 64 times bigger.

The volume scaled up by the original scale factor cubed.

Add these properties to your notebook

Example: Scaling Area and Volume

Example: Scaling Area and Volume