Hemisphere Formulas (Volume, Surface Area)

A hemisphere is half a sphere. Its volume is V = 2⁄3·πr³. Its curved surface is 2πr², and adding the flat circular face (πr²) gives a total surface area of 3πr².

Hemisphere formulas

Volume: $V = \tfrac{2}{3}\pi r^3$
Curved surface: $2\pi r^2$
Total surface area: $SA = 3\pi r^2$

where r = radius, V = volume, SA = total surface area

Volume

V = \tfrac{2}{3}\pi r^3

Curved surface

2\pi r^2

Total surface area

SA = 3\pi r^2

Worked example

A hemisphere of radius 3 has total surface area 27π ≈ 84.82 square units.

SA = 3\pi r^2 = 3\pi\cdot 9 = 27\pi \approx 84.82

Interactive hemisphere explorer

Drag a slider (or type a value, or use the arrow keys) and watch the diagram, the results, and the full step-by-step substitution update live.

Radius r

Volume V 134.04units³

Curved surface CSA 100.53units²

Total surface area SA 150.8units²

Step-by-step substitution

V = 2⁄3 πr³ = 2⁄3 · π · 4³ = 42.6667π ≈ 134.04
curved SA = 2πr² = 32π ≈ 100.53
total SA = 3πr² = 3 · π · 4² = 48π ≈ 150.8

Classroom use: hemisphere formulas

Who it's for: Grades 8–12 · Students working with composite solids, typically domes and rounded-end containers.

Learning objectives

After using this page, students will be able to:

Compute hemisphere volume as half a sphere's.
Compute total surface area as the curved half plus the flat circular base.
Explain why total surface area is not simply half a sphere's.

Suggested classroom activity

Ask for the surface area of a hemisphere and collect answers before revealing any. Most students halve 4πr² and forget the flat base. The explorer separates curved and base area, which makes the omission visible rather than merely corrected.

Standards alignment

Aligned to the Common Core State Standards for Mathematics. Codes are given exactly as published so they can be matched against state crosswalks.
Code	Standard
`8.G.C.9`	Know and use the formulas for the volumes of cones, cylinders, and spheres.
`HSG.GMD.A.3`	Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Free to use and adapt in class under the terms on our license page — no account, no sign-up, no ads. Content last reviewed August 2026.

Related & next steps

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Frequently asked questions

What is the total surface area of a hemisphere?

A hemisphere’s total surface area is 3πr²: the curved surface 2πr² plus the flat circular base πr². For radius 3, that is 27π ≈ 84.82 square units.

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