Cross-sections, Rotations, and Geometric Nets

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Presentation transcript:

Cross-sections, Rotations, and Geometric Nets Secondary Math 3 – Section 8.1

Names of Shapes Circle Square Rectangle Triangle Trapezoid Pentagon Hexagon Ellipse Octagon

Names of Solids Cube Prism Cylinder Sphere Pyramid Cone

What is a cross-section?

Identify the cross-section of this solid. Correct Answer: H

Identify the cross-section of this solid. Correct Answer: H

Identify the cross-section of this solid. Correct Answer: H

Identify the cross-section of this solid. Correct Answer: D (B if vertical)

Identify the cross-section of this solid. Correct Answer: F

Challenge Question Can you cut the cube with a plane and create a cross-section with: a) 3 sides b) 4 sides c) 5 sides d) 6 sides e) 7 sides f) 8 sides Cross-section Simulator a) yes; b) yes; c) yes; d) yes; e) no; f) no Since the cube has six faces (sides) only a six sided cross-section can be formed. Click on the link to see a way to visualize the cross-sections.

Geometric Nets – Example 1 Geometric nets describe the solid if it were “unfolded”

Geometric Nets – Example 2

Geometric Nets – Example 3

Two-dimensional Rotations What would happen if we rotated the function 𝑓 𝑥 = 1 4 𝑥 around the y-axis? If you shaded between the y-axis and f(x) and then rotated it around the y-axis you would have a cone. Radius would be 4 and height would be 1.

Two-dimensional Rotations What would you have to rotate to obtain this 3- dimensional solid? If you rotated a circle around a line not touching the circle you could create this donut.