Cross sections of 3 d figures
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Cross Sections of Thr ee-Dimensional Figure s
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Transcript of Cross sections of 3 d figures
Cross Sections of Three-Dimensional Figures
3-Dimensional figures can be cut by planes. When you cut a 3-D figure by a plane, the result is a 2-D figure.
A cross section is the shape formed when a plane intersects a 3D figure. Think of a very thin slice of the solid.
The cross-sections of 3-D figures are 2 dimensional figures you are familiar with like polygons and circlesTell the shape it makes when you cut the solid Look at the example on the next page to help your understanding.
A horizontal cross-section of a cone is a circle.
Can you describe a vertical cross-section of a cone?
A vertical cross-section of a cone is a triangle.
A water tower is built in the shape of a cylinder.
How does the horizontal cross-section compare to the vertical cross-section?
The horizontal cross-section is a circle.The vertical cross-section is a rectangle
Cross Sections
• Recall that bases are opposite faces that are parallel and congruent.
• To describe the relationship between the plane and the solid, it will be either:– Parallel to the base or – Perpendicular to the base
Parallel Cross Sections
Parallel Cross Sections
Perpendicular Cross Sections
Perpendicular Cross Sections
A plane slices through the cylinder below, parallel to the base. What is the resulting
cross-section?
A plane slices through the rectangular prism below, parallel to the base. What
is the resulting cross-section?
A plane slices through a cone and the resulting cross section is a triangle. Describe the
relationship between the plane and the cone.
Interactive Tools
Given a cone with a height of 6 m and a radius of 4 m, what is the area of the cross-section if
a plane slices the cone perpendicular to the base, through the center?
6m
4m
Find the area of the shaded cross-section of the trangular prism
Which figure has the same horizontal and vertical cross-sections?
A
B
C
D
Which figure does not have a triangle as one of its cross-sections?
A
B
C
D
Which is the vertical cross-section of the figure shown?
A Triangle B Circle C Square D Trapezoid
Which is the horizontal cross-section of the figure shown?
A Triangle B Circle C Square D Trapezoid
Which is the vertical cross-section of the figure shown?
A Triangle B Circle C Square D Trapezoid
