Table of Contents
Surface Area of Hemisphere formula
Introduction:
Surface area refers to the total area that covers the outer surface of a three-dimensional object. It includes the sum of all the areas of the object’s individual faces or surfaces. Surface area is typically measured in square units, such as square centimeters or square meters. It is an important concept in geometry and is used to determine the amount of material required to cover or wrap an object, as well as in various calculations and formulas related to shapes and structures.
What is a Hemisphere?
If a sphere is cut in half, it will lead to two hemispheres. Thus, a hemisphere is half a sphere. Its radius is the same as the radius of the sphere.
What is the Surface area of a hemisphere?
A hemisphere has a flat surface and a curved surface.
- Curved surface area of a hemisphere:
This is half of the surface area of the sphere
Curved surface area of hemisphere = 2πr2
It is important to note that this formula does not include the base of the hemisphere, as it is a flat circular shape and not part of the curved surface. Therefore, curved the surface area of a hemisphere only considers the curved portion.
- Total surface area of a hemisphere:
Total surface area of hemisphere = Area(Curved surface) + Area(Circle on top)
∴ Total surface area of hemisphere = 2πr2 + πr2
∴ Total surface area of hemisphere = 3πr2
Applications of surface Area of Hemisphere Formula:
The surface area of a hemisphere is often used in various applications, such as engineering, architecture, and geometry, to determine the amount of material needed to cover or enclose a hemisphere-shaped object. It provides a measure of the exposed surface of the hemisphere, which is useful for calculating quantities like paint needed or heat transfer in certain applications.
Conclusion:
In summary, the surface area of a hemisphere is the total area of its curved surface, and it is calculated using the formula 2πr2 and the total surface area is calculated using the formula 3πr2 This measure is valuable in determining material requirements and understanding the geometric properties of hemispheres.
Solved Examples on Surface Area of Hemisphere:
Example 1: Find the surface area of a hemisphere with a radius of 5 cm.
Solution:
The formula for the surface area of a hemisphere is Surface Area = 2πr², where ‘r’ is the radius.
Substituting the given value, we have:
Surface Area = 2π(5)²
Surface Area = 2π(25)
Surface Area = 50π cm²
Example 2: A metal hemisphere has a surface area of 154 sq. cm. Find its radius.
Solution:
The formula for the surface area of a hemisphere is Surface Area = 2πr².
Substituting the given value, we have:
154 = 2πr²
Dividing both sides by 2π, we get:
r² = 154 / (2π)
r² = 24.5 / π
Taking the square root of both sides, we get:
r = √(24.5 / π) cm
Therefore, the radius of the metal hemisphere is approximately 2.22 cm.
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Frequently Asked Questions on Surface Area of Hemisphere
What is the area and volume formula of hemisphere?
The formulas for the area and volume of a hemisphere are as follows: Area of Hemisphere: Surface Area = 2πr² Volume of Hemisphere: Volume = (2/3)πr³.
What is the CSA and TSA of a hemisphere?
In the case of a hemisphere, the CSA (Curved Surface Area) refers specifically to the surface area of the curved portion of the hemisphere. The formula to calculate the CSA of a hemisphere is 2πr², where r represents the radius of the hemisphere. On the other hand, the TSA (Total Surface Area) of a hemisphere encompasses the entire surface area, including both the curved surface area and the area of the flat circular base. The formula for the TSA of a hemisphere is derived by adding the CSA and the base area, resulting in TSA = 2πr² + πr², which simplifies to TSA = 3πr².
How does the surface area of hemisphere change when the radius is halved?
When the radius of a hemisphere is halved, the surface area of the hemisphere is reduced by a factor of four. This is because the surface area formula for a hemisphere, 2πr², is directly proportional to the square of the radius. Halving the radius results in reducing the area by a factor of 1/4, as (1/2)² = 1/4. Therefore, the surface area decreases significantly when the radius is halved.
How can you find the volume of a hemisphere?
The volume of a hemisphere can be calculated using the formula (2/3)πr³, where 'r' represents the radius of the hemisphere. This formula is derived by considering the hemisphere as half of a sphere and applying the formula for the volume of a sphere. By substituting the radius into the formula, the volume of the hemisphere can be determined.
What is the total surface area of the hemisphere of radius 7?
The total surface area of a hemisphere can be calculated using the formula 3πr², where 'r' is the radius of the hemisphere. In this case, with a radius of 7, the total surface area of the hemisphere would be 3π(7)² = 147π square units.
What is meant by curved surface area of hemisphere?
The curved surface area of a hemisphere refers to the total area of the curved surface that covers the hemisphere. In other words, it is the sum of all the areas of the curved regions on the surface of the hemisphere. The curved surface area does not include the flat circular base of the hemisphere.
What is the difference between area and surface area?
The difference between area and surface area lies in the context in which they are used. Area typically refers to the measure of the size of a two-dimensional shape or region. It represents the amount of space enclosed by the boundaries of the shape or region. For example, the area of a square is calculated by multiplying the length of one side by itself. Surface area, on the other hand, is used to describe the total area that covers the surface of a three-dimensional object. It includes the area of all the faces or surfaces of the object. For example, the surface area of a cube is calculated by adding up the areas of all its six square faces.
What is the Base Area of a Hemisphere?
The base area of a hemisphere refers to the area of the circular base of the hemisphere. In other words, it is the area of the flat, circular surface that forms the bottom part of the hemisphere. The base area is calculated using the formula for the area of a circle, which is πr2, where r represents the radius of the circular base.
