CROSS SECTION
Definition Of Cross Section
The plane figure obtained by the intersection of a solid by a plane is called as Cross-section.
More About Cross section
The figure obtained in the cross-section depends on the orientation of the plane cutting it.
Video Examples: Identify Cross Sections
Example of Cross section
In Figure 1 the prism is cut by a plane, which is parallel to the base. So, the intersection of the prism and the plane is a square cross-section. In Figure 2 the prism is cut by a plane, which is perpendicular to the base. So, the intersection of the prism and the plane is a rectangular cross-section.
Solved Example on Cross section
Ques: Describe the cross-section of the given figure.
Choices:
A. square
B. isosceles triangle
C. sector of a circle
D. rectangle
Correct Answer: B
Solution:
Step 1: Cross-section is a diagram or drawing that shows features transected by a given plane.
Step 2: The figure given is a cone. Insert a plane vertically through it.
Step 3: The cross-section is an isosceles triangle.
Step 4: The base of the triangle is the diameter of the circular base of the cone.
Step 5: The height of the triangle is the height of the cone.
Quick Summary
- Cross-sections are formed by slicing a 3D object with a plane.
- The shape of the cross-section depends on the orientation of the cutting plane.
- Different orientations yield different cross-sectional shapes.
⚠️ Common Mistakes
- Assuming the cross-section is always the same regardless of the cutting plane.
- Difficulty visualizing the 3D intersection.
- Confusing cross-sections with faces of the solid.
🌍 Real-World Uses
- Medical imaging techniques like CT scans and MRIs use cross-sections to visualize internal organs and tissues.
- Geologists analyze cross-sections of rock formations to understand the Earth's subsurface structure and composition.
- In manufacturing, cross-sections are used in engineering design to analyze the structural integrity of beams, pipes, and other components.
📋 Standards Alignment
CCSS.MATH.CONTENT.HSG.GMD.A.4CCSS.MATH.CONTENT.HSG.GMD.B.6
🔗 Related Links
🍎 Teacher Insights
Use physical models (play dough, clay) and string/wire to demonstrate cross sections. Encourage students to visualize the slicing process.🎓 Prerequisites
- Basic knowledge of 2D shapes
- Understanding of 3D solids (prisms, cones, etc.)
- Familiarity with planes and intersections
Check Your Knowledge
Q1: What shape is the cross-section of a cube cut parallel to its base?
Q2: What shape is the cross-section of a cone cut vertically through its apex?
Frequently Asked Questions
Q: What is a cross section?
A: A cross section is the shape you get when you slice through a 3D object with a plane.
Q: Does the orientation of the plane matter?
A: Yes, the angle at which the plane intersects the object determines the shape of the cross section.