UNIFORM CROSS SECTION
Definition Of Uniform Cross Section
A Uniform Cross Section is the cross section of the solid, parallel to base, such that the resulting figure has the same shape and size as that of the base of the figure.
More About Uniform Cross Section
Solids like pyramids and cones have slant heights and hence do not have uniform cross section.
Examples of Uniform Cross Section
The uniform cross section of the given prism is a square.
The uniform cross section of the given cylinder is a circle.
Video Examples: How to Find the Cross-Sectional Area of a Cylinder, Given the Diameter
Solved Example on Uniform Cross Section
Ques: Choose the uniform cross section of the solid shown.
Choices:
A. Figure 3
B. Figure 2
C. Figure 1
D. Figure 4
Correct Answer: B
Solution:
Step 1: The solid shown is a pentagonal prism
Step 2: The uniform cross section of the pentagonal prism is a pentagon
Step 3: So, Figure 2 is the uniform cross section of the solid shown
Quick Summary
- Uniform cross sections maintain the same shape and size as the base.
- Pyramids and cones do not have uniform cross sections due to their slant heights.
🍎 Teacher Insights
Use physical models to demonstrate cross sections. Cut fruits or vegetables to visualize different cross-sectional shapes.🎓 Prerequisites
- Basic shapes (squares, circles, pentagons)
- Understanding of prisms and cylinders
- Concept of a cross-section
Check Your Knowledge
Q1: Which of the following solids has a uniform cross section?
Frequently Asked Questions
Q: What shapes have uniform cross sections?
A: Prisms and cylinders have uniform cross sections.
Q: Are the cross sections the same at all points?
A: Yes, for solids with uniform cross sections, any cross-section parallel to the base has the same area and shape