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Volume of a hemisphere

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

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Student-friendly 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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete 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.

Definition

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

Example

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

Rule to remember

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

Memory hook

Hemisphere volume is half a sphere's volume.

Examples and method

Worked example

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

Method to apply

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

Diagram support

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.

How CBSE asks it

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

Avoid common mistakes

Common confusion

Students often write one-half of 4/3 πr³ as 1/3 πr³ instead of 2/3 πr³.

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.

Exam tip

A hemisphere is half a sphere, so its volume is 2/3 πr³, not 1/3 πr³.

Quick check

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

Use 2/3 πr³, because a hemisphere has half the volume of a sphere with the same radius.

Answer writing and exam use

1-mark answer

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

2-mark answer

The volume of a hemisphere is half the volume of a sphere with the same radius. Volume of a hemisphere = 2/3 πr³, where r is the radius of the hemisphere. For radius 6 cm, volume = 2/3 πr³ = 2/3 × π × 216 = 144π cm³.

3-mark answer

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. Volume of a hemisphere = 2/3 πr³, where r is the radius of the hemisphere. For r = 6 cm, volume = 2/3 πr³ = 2/3 × π × 216 = 144π cm³. Find the volume of a hemispherical bowl, dome, or half-ball using the given radius. 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.
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