Volume and surface area – Year 10 maths lesson
Lesson 7 of 37 in the Year 10 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 10 (ages 14–15) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 10 (ages 14–15)
- You need
- Paper, a pencil and this page
- Marked
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Can two shapes have the same volume but different surface areas?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Mixing up volume and surface area units. Volume: cm³. Area: cm².
- Missing hidden faces in surface area. Draw the net and label every face.
Tip for home: Work out how much a tin or a fish tank holds.
What your child will learn
We are learning to find the volume and surface area of prisms, cylinders, cones and spheres.
Success looks like
- I can find the volume of prisms and cylinders.
- I can find surface areas.
- I can use the formulas for cones and spheres.
Key words
- volume
- space inside a solid (cubic units)
- surface area
- total area of all the faces (square units)
- prism
- a solid with the same cross-section all along
- cross-section
- the shape you see when you slice across
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Find the volume of a tin or a cereal box by measuring, then check with water or rice.
The big ideas (for the adult)
The volume of a prism is the area of its cross-section × its length. A cylinder is a prism with a circle cross-section: πr²h.
Surface area is the total area of all the faces. Sketch the net to make sure no face is missed.
Cones and spheres have their own formulas: cone volume = ⅓πr²h; sphere volume = ⁴⁄₃πr³. Density = mass ÷ volume links volume to mass.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.
More practice
More Year 10 maths lessons
- Systematic listing and counting
- Standard form
- Laws of indices
- Surds
- Fractions, decimals and recurring decimals
- Circles: circumference, area, arcs and sectors
- Pythagoras' theorem
- Trigonometry: SOH CAH TOA
- Transformations
- Similarity and congruence
- Vectors
- Circle theorems
- Bearings
- 3-D shapes, plans and elevations
- Quartiles, box plots and spread
- Histograms
- Pie charts and time series graphs
- Scatter graphs and correlation
- Sampling
- Combined events and tree diagrams
- Simplifying expressions
- Expanding brackets
- Factorising
- Solving linear equations
- Inequalities
- Sequences and the nth term
- Straight-line graphs
- Simultaneous equations
- Quadratic equations
- Functions
- Graphs of functions
- Algebraic proof and identities
- Growth and decay
- Direct and inverse proportion
- Scale drawings and maps
- Rates of change from graphs
Curriculum
National Curriculum for England, Year 10: “calculate surface areas and volumes of spheres, pyramids, cones and composite solids”
GCSE subject content G17: “know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr²; calculate: perimeters of 2D shapes, including circles; areas of circles and composite shapes; surface area and volume of spheres, pyramids, cones and composite solids”
Contains public sector information licensed under the Open Government Licence v3.0.
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.