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Class 10 Maths · Chapter 12 · NCERT (jemh112)

Surface Areas and Volumes: common misconceptions

See the tempting mistake students make in Surface Areas and Volumes, why it feels right at first glance, and a worked visual example that shows the right idea.

The tempting mistake & worked visual

Do joined faces still count as outer surface?

Wrong

Add both full surface areas when two cubes are joined face to face.

Why it feels right. I calculate each solid separately and then add.

Right

Faces inside the join are excluded from the exposed area.

Worked example

Apart
□□□□□□
□□□□□□
Joined
□□□□□
□□□□□
The joined faces are now inside. Two groups of six exposed faces become two groups of five.
  1. Two unit cubes have 12 faces before joining.
  2. The two faces at the join become internal, leaving 10 exposed unit squares.

If your child says… (5 concept checks in this chapter)

As you work through Surface Areas and Volumes, listen for these everyday misunderstandings and use the prompt alongside each one.

1. Radius, height and slant height See how to teach this step →

If your child says… “The upright height and slant height are the same.”

Ask together
Which side lies opposite the right angle?
What’s true
The sloping route from tip to rim is longer than the perpendicular height.
2. Surface Area of a Combination of Solids See how to teach this step →

If your child says… “I add every surface of every part.”

Ask together
Could a paintbrush reach the circles without separating the parts?
What’s true
The touching circular faces lie inside the joined solid.
3. Surface Area of a Solid with a Hemispherical Depression See how to teach this step →

If your child says… “Scooping removes surface, so I subtract the hollow’s wall.”

Ask together
Could you coat the whole object while leaving this inner wall bare?
What’s true
Scooping exposes an inner wall that belongs in the surface area.
4. Volume of a Combination of Solids See how to teach this step →

If your child says… “I must subtract something where the parts join.”

Ask together
Does either part lose any material when their faces meet?
What’s true
Touching faces become hidden, but neither part loses volume.
5. Capacity and Volume Remaining See how to teach this step →

If your child says… “The cup still holds the same amount of water.”

Ask together
Where could the spilled water fit while the stone stays submerged?
What’s true
The submerged stone occupies space that water previously filled.

Use this chapter three ways

1 · Spot the trap (You are here)

Common misconceptions

Compare the tempting wrong rule with the right idea using a worked visual example before or after practice.

2 · Teach the concept

How to teach Surface Areas and Volumes →

For each idea: show it, ask before you tell, then say one line. (5 hands-on steps with photos and worked examples).

 3 · Check understanding

15 practice questions with answers →

Questions grouped by concept, including 10 with diagrams, each with a clear explanation.