Volume of a hemisphere
The volume of a hemisphere is half the volume of a sphere with the same radius.
Practice This ConceptMain explanation
Teacher explanation
Since a hemisphere is exactly half of a sphere, its volume is also half of the sphere's volume. Using the sphere formula and dividing by 2 gives the standard hemisphere volume formula. This is a common exam idea, especially in bowl and dome problems.
Example
For radius 6 cm, volume = 2/3 πr³ = 2/3 × π × 216 = 144π cm³.
Simple analogy
Hemisphere volume is half a sphere's volume.
Common confusion
Students often write one-half of 4/3 πr³ as 1/3 πr³ instead of 2/3 πr³.
Exam tip
A hemisphere is half a sphere, so its volume is 2/3 πr³, not 1/3 πr³.
Answer writing and exam use
1-mark use
Write the exact meaning of volume of a hemisphere in one clean line.
2-mark use
Define volume of a hemisphere and add one example or condition.
3-mark use
Explain volume of a hemisphere, show the method or example, and mention the common mistake.
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