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146 LearnersLast updated on December 11, 2025
Lateral Surface Area of a Hemisphere
A hemisphere is half of a sphere and consists of two surfaces: a curved surface and a flat circular base. The curved surface area represents the Lateral Surface of the Hemisphere. Consider a bowl cut exactly in half. The outer curved surface of the bowl is the lateral surface area of the hemisphere. The circular base is not included when considering only the lateral surface area.
Formula for Lateral Surface Area of a Hemisphere
We can find the lateral surface area of a hemisphere using the radius "r" of the hemisphere.
The lateral surface area is calculated using the formula, Area = 2πr².
How to Find Lateral Surface Area of Hemisphere
To find the Lateral Surface of a Hemisphere, follow these steps:
Step 1: Identify the given radius of the hemisphere.
Step 2: Ensure the radius is in the correct unit of measurement.
Step 3: Use the formula, Area = 2πr², to find the LSA of the hemisphere.
Step 4: Provide the calculated answer in square units.
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Common mistakes and how to avoid them in the Lateral Surface Area of a Hemisphere.
Here are some typical mistakes and how to avoid them when calculating the lateral surface area of a hemisphere:
Mistake 1
Forgetting to exclude the circular base.
Make sure to remember that the lateral surface area only includes the curved surface, not the base.
Mistake 2
Incorrectly squaring the radius.
Ensure that you correctly square the radius when applying it in the formula.
Double-check calculations before finalizing the answer.
Mistake 3
Not mentioning the units with the numerical value.
Always include the unit with your answer, even if the question doesn't specify a unit. It's standard to write "square units" as the unit.
Mistake 5
Confusing lateral surface area with total surface area.
Remember that lateral surface area refers only to the curved surface, while total surface area includes both the curved and circular surfaces.
Solved examples on Lateral Surface Area of a Hemisphere
Problem 1
What is the lateral area of a hemisphere with a radius of 5 cm?
157 cm²
Explanation
Given: Radius = 5 cm LSA = 2πr² = 2 × 3.14 × 5² = 2 × 3.14 × 25 = 157 cm²
Problem 2
If the radius of a hemisphere is q cm, and its curved surface area is 50 cmยฒ, find the value of q.
2.82 cm
Explanation
Given: Radius (r) = q cm CSA = 50 cm²
Using the formula: LSA = 2πr² 50 = 2 × 3.14 × q² 50 = 6.28q² q² = 50/6.28 q = √(50/6.28) q = 2.82 cm
Problem 3
Calculate the lateral surface area of a hemisphere with a radius of 7 cm.
308 cm²
Explanation
Given: Radius r = 7 cm LSA = 2πr² = 2 × 3.14 × 7² = 2 × 3.14 × 49 = 308 cm²
Problem 4
If a hemisphere has a curved surface area of 66 square units and the radius is 3 units, verify the calculation.
Correct calculation
Explanation
Given: Radius of hemisphere (r) = 3 units Curved surface area = 66 square units LSA = 2πr² = 2 × 3.14 × 3² = 2 × 3.14 × 9 = 56.52 square units
Problem 5
Find the radius of a hemisphere if its lateral surface area is 100 cmยฒ (Use ฯ = 22/7).
3.99 cm
Explanation
Let the radius be “r” cm.
LSA = 2πr² 100 = 2 × 22/7 × r² 100 = 44/7 × r² r² = (100 × 7)/44 r² = 15.91 r = √15.91 r = 3.99 cm
FAQโs on Lateral Surface Area
1.What is Lateral Surface Area?
2.How to calculate the lateral surface area.
3.Is the lateral surface area and the curved surface area the same?
4.How does the CSA change if the radius is doubled?
5.What is the difference between total surface area and lateral surface area?
Important Glossary for Lateral Surface Area
- Hemisphere: A 3D shape that represents half of a sphere, consisting of a curved surface and a flat circular base.
- Curved Surface Area (CSA): The area of the curved part of a 3D object, excluding any bases or flat surfaces.
- Radius: The distance from the center of the base to the edge of the circumference in a circle or sphere.
- π (Pi): A mathematical constant approximately equal to 3.14159, used to calculate areas related to circles and spheres.
- Square Units: A unit of area measurement, representing the area of a square with sides of one unit length.
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
