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Hemisphere Calculator: Volume, Surface Area, Formulas & Examples

Hemisphere Calculator: Volume, Surface Area, Formulas & Examples

Q: 3. How do I calculate the surface area of a hemisphere?

There are two types of surface areas for a hemisphere: The curved surface area is calculated using 2πr². The total surface area, which includes the curved surface and the flat circular base, is calculated using 3πr².

Q: 7. What is the difference between the curved surface area and the total surface area of a hemisphere?

The curved surface area of a hemisphere refers only to the area of the curved part, like the dome of a building. The total surface area includes both the curved surface area and the area of the flat circular base.

Q: 9. How do I find the radius of a hemisphere given its volume?

To find the radius, rearrange the volume formula: r = ³√(3V/(2π)). Substitute the known volume (V) and solve for 'r'. Remember to use consistent units for volume and radius.

How to Calculate the Volume and Surface Area of a Hemisphere

What is Hemisphere Calculator?

The Hemisphere Calculator instantly finds the volume and surface area of a solid hemisphere when you enter its radius. It is designed for students and professionals who want quick, accurate mensuration results.

This calculator eliminates manual calculation errors and provides detailed results in seconds. With its mobile-friendly design, it's perfect for learning or application on any device.

Formula Behind Hemisphere Calculator

The calculator applies the mensuration formulas: Volume V = (2/3) × π × r³, Curved Surface Area (CSA) = 2 × π × r², and Total Surface Area (TSA) = 3 × π × r², where r is the hemisphere’s radius and π ≈ 3.1416.

Hemisphere Conversion Table

Radius (cm)	Volume (cm³)	CSA (cm²)	TSA (cm²)
2	16.76	25.13	37.70
5	261.80	157.08	235.62
10	2094.40	628.32	942.48

Steps to Use Hemisphere Calculator

Enter the correct value.
Click "Calculate".
Instantly see accurate results.

Why Use Vedantu’s Hemisphere Calculator?

Save time and avoid errors: The tool gives the exact volume and area of a hemisphere with just a radius input, ensuring accuracy for homework or practical work.

It also displays the calculation steps and formulas, supporting learning, revision, and exam preparation, especially for chapters on 3D geometry and mensuration. Quickly access related tools, like the sphere or cube calculators, directly from this page.

Applications of Hemisphere Calculator

Use the calculator for geometry assignments, checking answers in competitive exams, or during science projects involving real-world shapes like domes, bowls, and Earth hemispheres.

Professionals in engineering or architecture can also use it for practical measurements, while students can deepen understanding through instant feedback. For more shapes and geometry tips, see Vedantu’s sphere volume or surface area resources.

Explore our Cube Calculator and find more help in 3D Solids Explained or browse other useful Algebra Topics.

FAQs on Hemisphere Calculator: Volume, Surface Area, Formulas & Examples

1. What is a hemisphere in geometry?

A hemisphere is a three-dimensional geometric shape that is exactly half of a sphere. It's formed by cutting a sphere in half through its center. It has a flat circular base and a curved surface. The curved surface is a portion of the sphere's surface.

2. What is the formula for the volume of a hemisphere?

The volume of a hemisphere is calculated using the formula: V = (2/3)πr³, where 'r' represents the radius of the hemisphere and π (pi) is approximately 3.1416.

3. How do I calculate the surface area of a hemisphere?

There are two types of surface areas for a hemisphere: The curved surface area is calculated using 2πr². The total surface area, which includes the curved surface and the flat circular base, is calculated using 3πr².

4. What are some real-world examples of hemispheres?

Hemispheres are found in many everyday objects and natural phenomena. Some examples include: the Earth's northern and southern hemispheres, bowls, domes on buildings, and the ends of some storage tanks. Many decorative items also utilize the hemisphere shape.

5. What are the properties of a hemisphere?

Key properties of a hemisphere include: It's a three-dimensional solid; it has a flat circular base; it possesses a curved surface that is part of a sphere's surface; its volume and surface area can be calculated using specific formulas; and it is symmetrical about a vertical axis passing through its center.

6. How can I use the Vedantu Hemisphere Calculator?

The Vedantu Hemisphere Calculator simplifies calculations. Simply input the radius of the hemisphere, and the calculator will instantly provide the volume and surface area. The results are accurate and easy to understand, saving you time and effort.

7. What is the difference between the curved surface area and the total surface area of a hemisphere?

The curved surface area of a hemisphere refers only to the area of the curved part, like the dome of a building. The total surface area includes both the curved surface area and the area of the flat circular base.

8. Where is the hemisphere formula used?

The hemisphere formula is applied in various fields including architecture (designing domes and other curved structures), engineering (calculating the capacity of tanks and containers), and various scientific applications where spherical or semi-spherical volumes need to be measured.

9. How do I find the radius of a hemisphere given its volume?

To find the radius, rearrange the volume formula: r = ³√(3V/(2π)). Substitute the known volume (V) and solve for 'r'. Remember to use consistent units for volume and radius.

10. Can I use the hemisphere calculator on my mobile phone?

Yes, the Vedantu Hemisphere Calculator is designed to be responsive and user-friendly on all devices, including mobile phones and tablets. You can access and use it conveniently on any device with an internet connection.

11. What are some common mistakes students make when calculating hemisphere volume or surface area?

Common mistakes include: using the incorrect formula (confusing sphere formulas with hemisphere formulas), making errors in calculations (especially when dealing with π and cubed values), and forgetting to consider both curved and flat surfaces when finding total surface area. Carefully reviewing the formulas and showing each step of your calculations can reduce mistakes.