The lateral area (curved surface area) of a hemisphere is L = 2πr2, where r is the radius. It is half of a sphere’s 4πr2 and leaves out the flat circular base. Example: r = 5 cm gives L = 2 × π × 25 ≈ 157.08 cm2. Add the base, πr2, to get the total surface area, 3πr2.
Reviewed by the Helping with Math Team · Updated 14 October 2026
What is the lateral area of a hemisphere?
Think of a dome, a bowl or half a coconut shell. The lateral area of a hemisphere is the area of its curved outside surface only. This page gives the formula, shows where it comes from, and works through examples in centimeters, meters and inches, with a calculator to check your answers.
Definition
The lateral area of a hemisphere refers to the curved surface area of a hemisphere, which is half of a sphere. It does not include the flat circular base.
Key terms
Hemisphere
A hemisphere is half of a sphere divided along a great circle, usually referred to as the equator.
Lateral area
The lateral area is the curved surface area of a solid, excluding its bases.
Lateral area formula
Surface Area is the total area covering the surface or outside part of a three-dimensional object. The formula 4πr2 is used to determine the surface area of a sphere, so half of that is the curved surface area of a hemisphere.
The word hemisphere has the prefix hemi, which came from the Greek term hēmi meaning “half.” So, the hemisphere means half of a sphere.
To get the lateral area of a hemisphere (L), we simply use the formula:
L = 2πr2
where:
r is the radius of the hemisphere.
π (pi) is about 3.14159. The answers below use the π key on a calculator.
Remember that the lateral surface area of a hemisphere does not include the area of the circular base. If we add the area of the base to the lateral surface area, we will get the total surface area.
Radius 5 cm. Lateral area 2π × 5² ≈ 157.08 cm². Base πr² ≈ 78.54 cm². Total surface area 3πr² ≈ 235.62 cm².
Worked examples
Example 1
Calculate the lateral area of a hemisphere with a radius of 5 cm.
Solution
L = 2πr2
L = 2 × π × 52
L ≈ 157.08 cm2
Therefore, the lateral area of the hemisphere is 157.08 cm2.
Always write the unit with your answer. Areas are in square units, such as cm2.
Example 2
Find the lateral surface area of a hemisphere with a radius of 7 cm.
Solution
L = 2πr2
L = 2 × π × 72
L ≈ 307.88 cm2
Therefore, the lateral surface area is 307.88 cm2.
Example 3
Determine the lateral surface area of a hemisphere whose diameter is 23 m.
Solution
The radius is half the diameter: 23 ÷ 2 = 11.5 m.
L = 2πr2
L = 2 × π × 11.52
L ≈ 830.95 m2
Therefore, the lateral surface area is 830.95 m2.
Real-life examples
Example 1
A hemispherical dome with a radius of 10 meters needs to be painted. How many square meters must be painted to cover the curved surface?
Solution
L = 2πr2
L = 2 × π × 102
L ≈ 628.32 m2
The painter must cover 628.32 square meters, the curved surface area of the curved surface area of the dome.
Example 2
A juice stall serves drinks in half coconut shells. Each half is a hemisphere with a diameter of 6 inches. What is the lateral surface area of one shell?
Solution
Since the diameter of the coconut is 6 inches, its radius is 3 inches. Calculating the lateral surface of its hemisphere, we have,
L = 2πr2
L = 2 × π × 32
L ≈ 56.55 in2
The curved surface of one half shell is 56.55 square inches.
Practice questions
A. Copy and complete the table. Round your answers to the nearest hundredth.
| Hemisphere | Radius | Lateral surface area |
|---|---|---|
| 1 | 12 m | |
| 2 | 8 in | |
| 3 | 5 cm | |
| 4 | 180 ft | |
| 5 | 5.5 yd |
B. Answer each problem.
- Calculate the lateral area of a hemisphere with a radius of 7 cm.
- Find the lateral area of a hemisphere with a diameter of 12 meters.
- A hemispherical container has a radius of 4 meters. How much material is needed to cover its curved surface?
- What is the lateral area of a hemisphere whose base has a circumference of 18.85 cm?
- A hemisphere has a lateral area of 100 cm2. Find its radius.
Answers. A: 1) 904.78 m2, 2) 402.12 in2, 3) 157.08 cm2, 4) 203,575.20 ft2, 5) 190.07 yd2. B: 1) 307.88 cm2; 2) r = 6 m, so 226.19 m2; 3) 100.53 m2; 4) r = 18.85 ÷ 2π ≈ 3 cm, so about 56.55 cm2; 5) r2 = 100 ÷ 2π ≈ 15.92, so r ≈ 3.99 cm.
More practice: lateral area of a hemisphere worksheets, surface area of a hemisphere worksheets and lateral surface area of a sphere worksheets.
For teachers: grade level and standards
Grade level
The concept of the lateral area of a hemisphere is typically introduced in middle school, around the 7th or 8th grade, and extends into high school geometry and pre-calculus courses.
Math domain
The lateral area of a hemisphere belongs to the domain of geometry, a branch of mathematics that deals with shapes, sizes, and properties of figures.
Common Core standards
The relevant Common Core Standards for studying the lateral area of a hemisphere are:
7.G.B.4: Know the formulas for the area and circumference of a circle and use them to solve problems.
8.G.C.9: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world problems.
G.GMD.A.1: Give an informal argument for the formulas for the circumference of a circle, the area of a circle, the volume of a cylinder, a pyramid, and a cone.
Lateral area of a hemisphere FAQs
What is the formula for the lateral surface area of a hemisphere?
L = 2πr², where r is the radius. For r = 7 cm, L = 2 × π × 49 ≈ 307.88 cm².
Why is it 2πr²?
A whole sphere has surface area 4πr². A hemisphere is half a sphere, so its curved surface is half of that: 2πr².
What is the difference between lateral area and total surface area of a hemisphere?
Lateral area is the curved part only, 2πr². Total surface area adds the flat circular base, πr², so it is 3πr².
How do I find the lateral area from the diameter?
Halve the diameter to get the radius first. A 6 inch diameter gives r = 3 in, so L = 2 × π × 9 ≈ 56.55 in².
How do I find the radius from the lateral area?
Divide the area by 2π, then take the square root. For L = 100 cm², r² = 100 ÷ 2π ≈ 15.92, so r ≈ 3.99 cm.
What is the volume of a hemisphere?
V = (2/3)πr³. Volume is in cubic units; lateral area is in square units.
