What Are the Four Hemispheres of the Earth?
Understanding the hemisphere helps you solve 3D geometry problems found in school exams, board tests, and real-world objects. Knowing its shape, properties, and formulas makes it easier to calculate areas and volumes, supporting quick mental maths and foundational geometry for competitive success.
Formula Used in Hemisphere
The standard formula for the volume of a hemisphere is: \( V = \frac{2}{3}\pi r^3 \), where r is the radius. The total surface area is \( 3\pi r^2 \), and the curved surface area is \( 2\pi r^2 \).
Here’s a helpful table to understand hemisphere properties more clearly:
Hemisphere Properties Table
| Property | Description | Example Value |
|---|---|---|
| Volume | \(\frac{2}{3}\pi r^3\) | 134.09 in3 (for r = 4 in) |
| Total Surface Area | \(3\pi r^2\) | 150.8 cm2 (for r = 4 cm) |
| Curved Surface Area | \(2\pi r^2\) | 100.5 cm2 (for r = 4 cm) |
| Flat Base Area | \(\pi r^2\) | 50.3 cm2 (for r = 4 cm) |
This table shows the hemisphere formulas and sample values for easy revision.
Meaning and Shape of a Hemisphere
A hemisphere is a 3D shape formed by cutting a sphere exactly into two equal halves along its diameter. It has one curved surface and one flat circular base. For example, a perfectly cut orange or a bowl represents a hemisphere. The flat side is called the base, which is a circle. Hemispheres have no edges or vertices.
To compare, a sphere has only a curved surface and no flat face. You can read more about spheres for deeper understanding.
Worked Example – Solving a Hemisphere Problem
Find the volume of a metal bowl that is shaped like a hemisphere with a radius of 7 cm. Take \(\pi = \frac{22}{7}\).
1. Write the volume formula of a hemisphere:2. Substitute the values (\( r = 7 \) cm, \( \pi = \frac{22}{7} \)):
3. Calculate \( 7^3 = 343 \):
4. Multiply \( \frac{22}{7} \times 343 = 1078 \):
5. Multiply by 2:
6. Divide by 3:
7. So, the volume of the hemispherical bowl is 718.67 cm3.
For more examples on volume, see Volume of Hemisphere.
Practice Problems
- Calculate the total surface area of a hemisphere with radius 5 cm.
- What is the difference between a hemisphere and a sphere?
- If the volume of a hemisphere is 36π cm3, find its radius.
- Is a bowl with a flat base a hemisphere? Why or why not?
You can practice more questions in Surface Area and Volumes with stepwise solutions.
Common Mistakes to Avoid
- Writing or using the sphere formula instead of the hemisphere formula.
- Forgetting to add the base area when calculating the total surface area.
- Using diameter instead of radius in the formula, which changes the result.
- Mixing up curved surface area and total surface area.
Real-World Applications
The concept of hemisphere is seen in everyday objects such as bowls, domes, and even in Earth's divisions—northern or southern hemisphere—used in geography. In maths, hemispheres help solve practical problems on volume and surface area. Vedantu helps students explore these real-life uses for deeper concept clarity.
If you want to connect more geometric shapes, visit: 3D Shapes, Solid Geometry, or Solid Figure pages for visual learning.
We explored the idea of hemisphere, its formulae, problem-solving steps, and real-life importance. Practise more with Vedantu and check out the sphere formula for comparison. Mastering hemispheres ensures you can tackle mensuration, geometry, and application-based questions with confidence.
FAQs on What Is a Hemisphere? Definition and Examples for Students
1. What does hemisphere mean?
Hemisphere refers to a half of a spherical object, such as a globe or planet. On Earth, a hemisphere is one of the two equal parts formed by dividing the planet with an imaginary line such as the equator or a meridian. In the context of the brain, a hemisphere is one of the two halves of the brain (left and right).
2. What are the 4 hemispheres of the Earth?
The four hemispheres of the Earth are:
- Northern Hemisphere (north of the Equator)
- Southern Hemisphere (south of the Equator)
- Eastern Hemisphere (east of the Prime Meridian)
- Western Hemisphere (west of the Prime Meridian)
3. What hemisphere is the United States in?
The United States is located in the Northern Hemisphere and primarily in the Western Hemisphere, as it lies north of the Equator and west of the Prime Meridian.
4. What is a hemisphere in the brain?
A hemisphere of the brain refers to either the left or right half of the brain. The two hemispheres manage different functions and are connected by the corpus callosum. The left hemisphere often controls language and logic, while the right hemisphere is linked to creativity and spatial abilities.
5. What is hemispherectomy?
Hemispherectomy is a rare surgical procedure in which one cerebral hemisphere (half of the brain) is removed or disabled to treat severe brain disorders like epilepsy. It is usually performed only when other treatments fail.
6. How do you calculate the volume of a hemisphere?
The volume of a hemisphere is calculated using the formula: V = (2/3)πr3, where r is the radius of the hemisphere. This formula gives the space inside half a sphere.
7. What is the shape of a hemisphere?
A hemisphere is shaped like half of a sphere. It has a flat circular base and a curved surface, resembling a dome or bowl.
8. Describe a hemisphere in geography.
In geography, a hemisphere is any half of the world divided by either the Equator or the Prime Meridian. This helps in studying weather patterns, climate zones, and the distribution of land and water on Earth.
9. What is the difference between the Northern and Southern Hemispheres?
The Northern Hemisphere is north of the Equator and contains most of Earth's landmass, including continents such as North America, Europe, and most of Asia. The Southern Hemisphere lies south of the Equator and is dominated by oceans and includes continents like Australia, much of South America, and parts of Africa. The seasons are opposite in each hemisphere.
10. What is a hemisphere map?
A hemisphere map shows one half of the world, either north/south or east/west, depending on the division. It is useful for focusing on a particular region, continent, or set of countries within a specific hemisphere.
11. What are the applications of the hemisphere formula?
The hemisphere formula is used to find the volume and surface area of hemispherical objects, such as bowls, domes, tanks, and in solving geometry problems in school exams. It helps in practical fields like construction, architecture, and engineering.
12. What is the surface area formula for a hemisphere?
The total surface area of a hemisphere is given by the formula: Surface Area = 3πr2, where r is the radius. This includes both the curved surface and the base area.
