HEMISPHERE
Definition Of Hemisphere
Hemisphere is the exact half of a sphere.
More About Hemisphere
When a plane cuts across a sphere at its center, it forms two hemispheres
Surface area of a hemisphere of radius r is given by 2pr2
Volume of a hemisphere of radius r is given by 2/3pr3
Video Examples: Hemisphere
Example of Hemisphere
The upper and lower parts of the sphere are equal halves.
Solved Example on Hemisphere
Ques: Which of these shows a hemisphere?
Choices:
A. Figure 2
B. Figure 1
C. Figure 4
D. Figure 3
Correct Answer: D
Solution:
Step 1: Hemisphere is the exact half of a sphere.
Step 2: The figure shown in Figure 1 is a cone. So, Figure 1 is not a hemisphere
Step 3: The figure shown in Figure 2 is a circle. So, Figure 2 is not a hemisphere
Step 4: The figure shown in Figure 3 is exactly the half of a sphere. So, Figure 3 is a hemisphere
Step 5: The figure shown in Figure 4 is a cylinder. So, Figure 4 is not a hemisphere
Step 6: So, Figure 3 is the hemisphere as it is exactly half of the sphere.
Quick Summary
- A hemisphere is half a sphere.
- It is formed by cutting a sphere through its center.
- The surface area of a hemisphere is 2πr².
- The volume of a hemisphere is (2/3)πr³.
🍎 Teacher Insights
Use real-world examples like halved oranges or domes to illustrate hemispheres. Emphasize the relationship between the formulas for a sphere and a hemisphere. Use visual aids to show the plane cutting through the sphere.🎓 Prerequisites
- Understanding of spheres
- Basic knowledge of area and volume
- Familiarity with the concept of radius
Check Your Knowledge
Q1: Which of the following is a hemisphere?
Q2: The radius of a hemisphere is 5 cm. What is its volume?
Frequently Asked Questions
Q: What is the difference between a sphere and a hemisphere?
A: A sphere is a 3-dimensional object, like a ball. A hemisphere is exactly half of a sphere.
Q: How is a hemisphere formed?
A: A hemisphere is formed when a plane cuts across a sphere at its center.