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CraftExam
medium difficulty6 min

Combination of solids

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

In one line: Joined solids: add volumes, hide joints.

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Understand it

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.

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.

Formula and rule

For a combination of solids, total volume = sum of component volumes.

For outer surface area, count only exposed parts and exclude hidden joining faces.

See it worked out

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

Worked example

  1. 1For a toy made from a cylinder and a hemisphere, add the cylinder volume and hemisphere volume to get total volume.
  2. 2For outer area, add only the curved and exposed flat parts.

Method you can reuse

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

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

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.

Don't mix this up

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

Exam tip

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

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 or outside surface area of toys, caps, tanks, containers, or decorative objects made from joined solids.
  1. 1

    Enough for 1 mark

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

  2. 2

    Add for 2 marks

    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.

  3. 3

    Add for 3 marks

    Many real objects are not one single solid.

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