Hemisphere volume and curved surface
Half a sphere is not half the formulas in every case — check whether the flat face is included.
Key formulas
Volume halves cleanly
Full sphere (4/3)πr³ → hemisphere (2/3)πr³.
Surface depends on the question
Curved surface alone is 2πr². If the flat circular face is included, add πr² to get 3πr².
Example
r = 6. Volume = (2/3)π(216)=144π. Total surface including base = 3π(36)=108π.
Worked example
Worked example
Problem. A solid hemisphere has radius 6 cm. Find its volume and total surface area (including the flat face) in terms of π.
Solution. V = (2/3)πr³ = (2/3)π × 216 = 144π cm³. Total surface = 3πr² = 3π × 36 = 108π cm².
Read the wording
“Curved surface area” ≠ “total surface area”.
Review quiz
Hemisphere radius 3. Volume is:
Practice questions
- r=3. Find volume in terms of π.
- r=5. Find total surface including the flat face.
Study notes
Is a bowl the same?
A thin bowl may ignore thickness; still decide if the rim face is counted.
More in Spatial Geometry
- Pyramid volume: identify the base and perpendicular height
- Distance from a point to a plane using volume
- Finding the angle between a line and a plane
- Writing the equation of a plane in 3D
- Cylinder volume and curved surface area
- Cone volume when slant height is given
- Prism volume from a cross-section
- Sphere volume without the fear of π