Ice cream factories test how consistently the ingredients are distributed through each carton by cutting cartons in half for a good view. Describe the 2D figures that result from slicing a carton vertically or diagonally through the top & side. How do you determine the shape that results from slicing a 3D solid?

In this lesson, you will learn how to visualize the 2D cross- sections of cylinders by analyzing if a plane intersects with straight or curved surfaces.

Core Lesson Effect of slicing plane Where a plane intersects faces, a 2D figure results

Let’s Review Identify characteristics of the solid Bases Lateral surface (face) Edges

Core Lesson Distance from center is constant. Therefore it’s a circle Horizontal Cross-section r r Slices parallel to base are congruent to base

Vertical Cross-section Vertical slice always creates a parallelogram

A Common Misunderstanding A diagonal cross-section creates a circle Circles are only created by horizontal cross-sections

Core Lesson Distance from center is not constant Actually an ellipse Diagonal Cross-section b a

Core Lesson Diagonal Cross-section Types of faces intersected determines types of edges on 2D figure

Intersects 2 arcs & 2 parallel lines Diagonal Cross-section

Core Lesson Ice cream factories test how consistently the ingredients are distributed through each carton by cutting cartons in half for a good view. Describe the 2D figures that result from slicing a carton vertically or diagonally through the top & side. Vertical: rectangle Diagonal: half-moon

In this lesson, you have learned how to visualize the 2D cross- sections of cylinders by analyzing if a plane intersects with straight or curved surfaces.