C
CraftExam
medium difficulty5 min

Volume of a hemisphere

The volume of a hemisphere is half the volume of a sphere with the same radius.

In one line: Hemisphere volume is half a sphere's volume.

Practice This Concept

Understand it

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.

Formula and rule

Volume of a hemisphere = 2/3 πr³, where r is the radius of the hemisphere.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

For r = 6 cm, volume = 2/3 πr³ = 2/3 × π × 216 = 144π cm³.

Method you can reuse

  1. 1Identify the radius.
  2. 2Cube the radius carefully.
  3. 3Multiply by 2/3 and π.
  4. 4Simplify.
  5. 5Write the answer in cubic units.

Sketch it in your answer

Draw a hemisphere and mark the radius from the center of the base circle to the curved surface. Show that the volume depends only on the radius.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A hemispherical solid has radius 6 cm. Which formula gives its volume?

Think first, then show answer
Use 2/3 πr³, because a hemisphere has half the volume of a sphere with the same radius.

Common wrong answer

A common wrong answer is 1/3 πr³. That is too small because a hemisphere is half of a sphere, not one-third of it.

Don't mix this up

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.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Find the volume of a hemispherical bowl, dome, or half-ball using the given radius.
  1. 1

    Enough for 1 mark

    The volume of a hemisphere is half the volume of a sphere with the same radius.

  2. 2

    Add for 2 marks

    Example: For radius 6 cm, volume = 2/3 πr³ = 2/3 × π × 216 = 144π cm³.

  3. 3

    Add for 3 marks

    Using the sphere formula and dividing by 2 gives the standard hemisphere volume formula.

MCQ Quiz

Practice this concept with focused MCQs

Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.

10 MCQs5 MinutesInstant Results
Practice This Concept

Help improve this page

Found something confusing, incorrect, or missing?

Practice This Concept