# Total Surface Area of Hemisphere

## Total Surface Area of Hemisphere

A sphere is a three-dimensional object where every point on its outer surface is at an equal distance from its center. When a plane intersects the sphere exactly through its center, it divides the sphere into two congruent halves, each called a hemisphere. By joining these two hemispheres together, a complete sphere is formed.

### Area of the Hemisphere

We can easily determine the surface area of a hemisphere due to the circular nature of the sphere's base. The surface area of a hemisphere can be divided into two main types: the total surface area and the curved surface area. These two categories differ in what they encompass.

### Area of Curved Surface

The curved surface area is the area of the hemisphere's outer

surface.

### Surface Area Total

The total surface area of a hemisphere includes both the area of its curved surface and the area of its circular base. Since a hemisphere is half of a sphere, we can start by finding the curved surface area (CSA) of the hemisphere.

The curved surface area of a sphere is given by the formula:

CSA of sphere = 4πr^{2}

Since the hemisphere is half of the sphere, its curved surface area is:

CSA of hemisphere = (1/2) × 4πr^{2} = 2πr^{2}

Thus, the curved surface area of a hemisphere is:

Curved surface area = 2πr^{2} square units

Next, we need to include the area of the circular base. The area of a circle is given by the formula:

Area of base = πr^{2}

Therefore, the total surface area (TSA) of the hemisphere, which includes both the curved surface area and the base area, is:

TSA = 2πr^{2} + πr^{2} = 3πr^{2}

In summary:

Total surface area of a hemisphere = 3πr^{2} square units

Here, π (pi) is a constant approximately equal to 3.14, and r represents the radius of the hemisphere.

## Surface Area of a Hemisphere Example

To calculate the surface area of a hemisphere with a radius of 4 cm:

### Curved Surface Area (CSA):

Formula: CSA = 2πr^{2}

Substitute the radius (r = 4 cm):

CSA = 2 × 3.14 × 4 × 4

CSA = 3.14 × 32

CSA = 100.48 square centimeters

### Total Surface Area (TSA):

Formula: TSA = 3πr^{2}

Substitute the radius (r = 4 cm):

TSA = 3 × 3.14 × 4 × 4

TSA = 3.14 × 48

TSA = 150.72 square centimeters

Therefore, the curved surface area of the hemisphere is 100.48 square centimeters, and the total surface area is 150.72 square centimeters.

#### Related Links

- Derivative of Inverse Trigonometric functions
- Decimal Expansion Of Rational Numbers
- Cos 90 Degrees
- Factors of 48
- De Morgan’s First Law
- Counting Numbers
- Factors of 105
- Cuboid
- Cross Multiplication- Pair Of Linear Equations In Two Variables
- Factors of 100
- Factors and Multiples
- Derivatives Of A Function In Parametric Form
- Factorisation Of Algebraic Expression
- Cross Section
- Denominator
- Factoring Polynomials
- Degree of Polynomial
- Define Central Limit Theorem
- Factor Theorem
- Faces, Edges and Vertices
- Cube and Cuboid
- Dividing Fractions
- Divergence Theorem
- Divergence Theorem
- Difference Between Square and Rectangle
- Cos 0
- Factors of 8
- Factors of 72
- Convex polygon
- Factors of 6
- Factors of 63
- Factors of 54
- Converse of Pythagoras Theorem
- Conversion of Units
- Convert Decimal To Octal
- Value of Root 3
- XXXVII Roman Numerals
- Continuous Variable
- Different Forms Of The Equation Of Line
- Construction of Square
- Divergence Theorem
- Decimal Worksheets
- Cube Root 1 to 20
- Divergence Theorem
- Difference Between Simple Interest and Compound Interest
- Difference Between Relation And Function
- Cube Root Of 1728
- Decimal to Binary
- Cube Root of 216
- Difference Between Rows and Columns
- Decimal Number Comparison
- Data Management
- Factors of a Number
- Factors of 90
- Cos 360
- Factors of 96
- Distance between Two Lines
- Cube Root of 3
- Factors of 81
- Data Handling
- Convert Hexadecimal To Octal
- Factors of 68
- Factors of 49
- Factors of 45
- Continuity and Discontinuity
- Value of Pi
- Value of Pi
- Value of Pi
- Value of Pi
- 1 bigha in square feet
- Value of Pi
- Types of angles
- Total Surface Area of Hemisphere
- Total Surface Area of Cube
- Thevenin's Theorem
- 1 million in lakhs
- Volume of the Hemisphere
- Value of Sin 60
- Value of Sin 30 Degree
- Value of Sin 45 Degree
- Pythagorean Triplet
- Acute Angle
- Area Formula
- Probability Formula
- Even Numbers
- Complementary Angles
- Properties of Rectangle
- Properties of Triangle
- Co-prime numbers
- Prime Numbers from 1 to 100
- Odd Numbers
- How to Find the Percentage?
- HCF Full Form
- The Odd number from 1 to 100
- How to find HCF
- LCM and HCF
- Calculate the percentage of marks
- Factors of 15
- How Many Zeros in a Crore
- How Many Zeros are in 1 Million?
- 1 Billion is Equal to How Many Crores?
- Value of PI
- Composite Numbers
- 100 million in Crores
- Sin(2x) Formula
- The Value of cos 90°
- 1 million is equal to how many lakhs?
- Cos 60 Degrees
- 1 Million Means
- Rational Number
- a3-b3 Formula with Examples
- 1 Billion in Crores
- Rational Number
- 1 Cent to Square Feet
- Determinant of 4×4 Matrix
- Factor of 12
- Factors of 144
- Cumulative Frequency Distribution
- Factors of 150
- Determinant of a Matrix
- Factors of 17
- Bisector
- Difference Between Variance and Standard Deviation
- Factors of 20
- Cube Root of 4
- Factors of 215
- Cube Root of 64
- Cube Root of 64
- Cube Root of 64
- Factors of 23
- Cube root of 9261
- Cube root of 9261
- Determinants and Matrices
- Factors of 25
- Cube Root Table
- Factors of 28
- Factors of 4
- Factors of 32
- Differential Calculus and Approximation
- Difference between Area and Perimeter
- Difference between Area and Volume
- Cubes from 1 to 50
- Cubes from 1 to 50
- Curved Line
- Differential Equations
- Difference between Circle and Sphere
- Cylinder
- Difference between Cube and Cuboid
- Difference Between Constants And Variables
- Direct Proportion
- Data Handling Worksheets
- Factors of 415
- Direction Cosines and Direction Ratios Of A Line
- Discontinuity
- Difference Between Fraction and Rational Number
- Difference Between Line And Line Segment
- Discrete Mathematics
- Disjoint Set
- Difference Between Log and Ln
- Difference Between Mean, Median and Mode
- Difference Between Natural and whole Numbers
- Difference Between Qualitative and Quantitative Research
- Difference Between Parametric And Non-Parametric Tests
- Difference Between Permutation and Combination

## Frequently Asked Questions on Total Surface Area of Hemisphere

The surface area of a hemisphere has two parts - the curved surface area (CSA) and the total surface area (TSA). The CSA is 2πr^2, while the TSA is 3πr^2, where r is the radius of the hemisphere. The volume of a hemisphere is (2/3)πr^3.

The curved surface area (CSA) of a hemisphere is the area of the curved outer surface, and it is calculated as 2πr^2. The total surface area (TSA) includes the CSA plus the area of the circular base, which is calculated as 3πr^2.

The formula for the total surface area (TSA) of a hemisphere is 3πr^2, where r is the radius of the hemisphere. This includes the curved surface area (2πr^2) plus the area of the circular base (πr^2).

The total surface area (TSA) of a hemisphere is 3πr^2 because it includes both the curved surface area (2πr^2) and the area of the circular base (πr^2). The TSA represents the complete outer surface area of the hemisphere.

The total surface area (TSA) of a cylinder is the sum of the curved surface area (2πrh) and the area of the two circular bases (2πr^2).

The TSA of a hemisphere is 3πr^2, where r is the radius. This includes the curved surface area (2πr^2) and the area of the circular base (πr^2).