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Combination of solids

A combination of solids is a shape formed by joining two or more simple solids together.

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Student-friendly explanation

Many real objects are not one single solid. They may be made from a cylinder and a hemisphere, a cone on a cylinder, or other joined parts. In such questions, the volume is found by adding the volumes of all parts, while the outer surface area includes only the exposed surfaces and excludes the joining faces.

How to write this in exams

  1. 1

    Start with the exact idea

    A combination of solids is a shape formed by joining two or more simple solids together.

  2. 2

    Then show how to use it

    1. Split the figure into known solids. 2. Write each formula separately. 3. Add volumes for capacity questions. 4. For surface area, count only exposed surfaces. 5. Ignore hidden joints and write the final unit correctly.

  3. 3

    Add one concrete example

    A toy may consist of a cylinder with a hemispherical top. Its total volume is the volume of the cylinder plus the volume of the hemisphere, but the circular face where they join is not counted in outer surface area.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is to include the joined circular face in surface area or to subtract one solid from another without reason.

Definition

A combination of solids is a shape formed by joining two or more simple solids together.

Example

A toy may consist of a cylinder with a hemispherical top. Its total volume is the volume of the cylinder plus the volume of the hemisphere, but the circular face where they join is not counted in outer surface area.

Rule to remember

For a combination of solids, total volume = sum of component volumes. For outer surface area, count only exposed parts and exclude hidden joining faces.

Memory hook

Joined solids: add volumes, hide joints.

Examples and method

Worked example

For a toy made from a cylinder and a hemisphere, add the cylinder volume and hemisphere volume to get total volume. For outer area, add only the curved and exposed flat parts.

Method to apply

1. Split the figure into known solids. 2. Write each formula separately. 3. Add volumes for capacity questions. 4. For surface area, count only exposed surfaces. 5. Ignore hidden joints and write the final unit correctly.

Diagram support

Sketch the full object and mark each component solid separately. Circle the joined face so students remember it is hidden and should not be counted in outer surface area.

How CBSE asks it

Find the volume or outside surface area of toys, caps, tanks, containers, or decorative objects made from joined solids.

Avoid common mistakes

Common confusion

Students often count hidden joining surfaces or forget to add one of the component volumes.

Common wrong answer

A common wrong answer is to include the joined circular face in surface area or to subtract one solid from another without reason.

Exam tip

First split the object into simple solids, then add volumes or exposed areas carefully.

Quick check

A solid object is made by joining a cylinder and a hemisphere. What should be ignored while finding the outer surface area?

The hidden circular joining face should be ignored, because only the exposed outer surfaces are counted in surface area.

Answer writing and exam use

1-mark answer

A combination of solids is a shape formed by joining two or more simple solids together.

2-mark answer

A combination of solids is a shape formed by joining two or more simple solids together. For a combination of solids, total volume = sum of component volumes. For outer surface area, count only exposed parts and exclude hidden joining faces. A toy may consist of a cylinder with a hemispherical top. Its total volume is the volume of the cylinder plus the volume of the hemisphere, but the circular face where they join is not counted in outer surface area.

3-mark answer

Many real objects are not one single solid. They may be made from a cylinder and a hemisphere, a cone on a cylinder, or other joined parts. In such questions, the volume is found by adding the volumes of all parts, while the outer surface area includes only the exposed surfaces and excludes the joining faces. For a combination of solids, total volume = sum of component volumes. For outer surface area, count only exposed parts and exclude hidden joining faces. For a toy made from a cylinder and a hemisphere, add the cylinder volume and hemisphere volume to get total volume. For outer area, add only the curved and exposed flat parts. Find the volume or outside surface area of toys, caps, tanks, containers, or decorative objects made from joined solids. A common wrong answer is to include the joined circular face in surface area or to subtract one solid from another without reason.
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