Lateral Surface Area of a Hemisphere
2026-02-28 17:44 Diff
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Last updated on December 11, 2025

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.

What is the Lateral Surface Area of a Hemisphere?

The curved surface area of the hemisphere is considered the lateral surface area of a hemisphere.

It is the area of the outer curved surface excluding the circular base.

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:

Problem 1

What is the lateral area of a hemisphere with a radius of 5 cm?

Okay, lets begin

157 cm²

Explanation

Given: Radius = 5 cm LSA = 2πr² = 2 × 3.14 × 5² = 2 × 3.14 × 25 = 157 cm²

Well explained 👍

Problem 2

If the radius of a hemisphere is q cm, and its curved surface area is 50 cm², find the value of q.

Okay, lets begin

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

Well explained 👍

Problem 3

Calculate the lateral surface area of a hemisphere with a radius of 7 cm.

Okay, lets begin

308 cm²

Explanation

Given: Radius r = 7 cm LSA = 2πr² = 2 × 3.14 × 7² = 2 × 3.14 × 49 = 308 cm²

Well explained 👍

Problem 4

If a hemisphere has a curved surface area of 66 square units and the radius is 3 units, verify the calculation.

Okay, lets begin

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

Well explained 👍

Problem 5

Find the radius of a hemisphere if its lateral surface area is 100 cm² (Use π = 22/7).

Okay, lets begin

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

Well explained 👍

FAQ’s on Lateral Surface Area

1.What is Lateral Surface Area?

The area consumed by the curved surface of a hemisphere is called the lateral surface area of a hemisphere.

2.How to calculate the lateral surface area.

The Lateral Surface Area of a hemisphere can be calculated using the formula: Area = 2πr²

3.Is the lateral surface area and the curved surface area the same?

Yes, for a hemisphere, they both refer to the same thing.

4.How does the CSA change if the radius is doubled?

If the radius is doubled, the CSA becomes four times larger, as it depends on the square of the radius.

5.What is the difference between total surface area and lateral surface area?

The lateral surface area only includes the curved part, while the total surface area includes both the curved surface and the circular base.

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.

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Seyed Ali Fathima S

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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.

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