NCERT Mathematics, Class 10, textbook pages 161–170

How to help your child with Class 10 Maths Chapter 12, Surface Areas and Volumes, at home

Combinations of solids, explained for parents: a 45-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

cone + hemisphere

NCERT Class 10 Maths Chapter 12 Surface Areas and Volumes: what it teaches

Your teen finds surface areas and volumes of combined solids like a cone on a hemisphere or a cylinder with hemispherical ends, choosing which surfaces count.

Why it matters later. Mensuration is used in engineering, packaging and Class 11–12 calculus (volumes).

See it: this chapter in pictures

cylinder: V = πr²hcone: V = ⅓πr²hsphere: V = 4/3 πr³
Keep a formula sheet.
r = 7, h = 10V = 22/7 × 49 × 10= 1540 cm³
Substitute carefully.
joined solids:add visible surfaces onlyhidden faces don’t count
Count only what could be painted.

You need

  • a formula sheet
  • objects: ice-cream cone, capsule, tent pictures
  • a calculator

Tonight’s 45 minutes

  1. List the formulas for cube, cuboid, cylinder, cone, sphere, hemisphere.
  2. A toy is a cone on a hemisphere (r = 3.5 cm, total height 15.5 cm). Find its surface area.
  3. Find the volume of a capsule shape.
  4. Discuss which surfaces are hidden when solids are joined.

Words to use

  • curved surface area
  • total surface area
  • volume
  • hemisphere
  • frustum

Watch for

  • Adding hidden faces to surface area. Only count surfaces you could paint.
  • Radius/diameter mix-ups. Write r clearly for every part.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouCone on a hemisphere: which surfaces?

Your childThe cone’s curved surface and the hemisphere’s curved surface.

A game for this week: Object measurer

  1. Pick a household object made of simple solids.
  2. Measure it.
  3. Calculate volume and surface area.
  4. Compare with estimates.

A 5-day plan, 45 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Water tanks.
  • Ice-cream cones.
  • Medicine capsules.
  • Grain silos.

Quick check

Ask these at the end of the week. Tap to see the answer.

Volume of a cylinder r = 7, h = 10?

1540 cm³.

CSA of a hemisphere?

2πr².

Do you add the joined circle in a cone-on-hemisphere toy?

No, it’s hidden.

Ready for the next chapter when your child…

  • Recalls formulas.
  • Splits combined solids.
  • Calculates SA and volume correctly.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 10). See the full Class 10 parent guide for every chapter.

Questions parents ask

Which formulas are essential?

Cylinder, cone, sphere and hemisphere surface area and volume.

How do I handle combined solids?

Split into parts and add only visible surfaces.

Is frustum included?

Check the current syllabus; it may be reduced.