Circles, surface area and volume

Discover our collection of GCSE maths circles, surface area and volume lessons, activities, powerpoints and notes. These resources are hand-picked by the Tes Maths Panel for their relevance to the 9-1 specifications - use them for planning, homework and revision.

This page contains the very best resources for teaching sections G9, G16 to G18 from the GCSE maths specification (first examined in 2017), combining structured lessons and engaging activities. It is not just remembering all the formulae associated with circles and volumes that is the key, but being able to apply them successfully in a variety of contexts. These lovely resources should help with that.

View more Geometry and Measures topics

Circumference of a circle

Circumference of Circles Whole lesson and resources

Here is a standard lesson I have used with so many classes as it works really well and progression is apparent through the perimeter of shapes involving circles.

As always please feel free to use and once used please take the time to review it.... I always want to improve my resources so any feedback would be greatly received.

Check out my store for more... enjoy and hope it is of use!
By Yougoteach

Circumference of a Circle FULL LESSON (Grade 3/4)

I made this for an observation lesson with a low ability year 11 class.

You will need to print off the Quiz Quiz Trade (on excel). There are also built in progress checks which I used on mini whiteboards.

The countdown timer that I've attached I have downloaded from the website below.
By arthompson1987

Rope around the world

Basic PowerPoint for the age old 'rope around the world' problem. Useful as a starter after studying circumferences.
By tonymcaleese

Introduction to Pi lesson

Circles, circumference.
This lesson allows students to discover the value of Pi by using the worksheet. It includes some history and practice questions for circumference only. Can be used with mini-whiteboards for starter (possibly for practice questions as well).
The worksheet attached is not of good quality - you can find the original on TES. However, I have now added a worksheet with a table allowing students to measure actual 3D cylinders that can be a little more fun.
By keren_s

Area of a circle

Area of a circle, semi circle, quarter and composite - KS3

Y9 class - finding all types of circle's areas, with functional questions and activities.
By prabhleenkaur

Murder Mystery - Circles

Adapted from another murder mystery on circles on here - brought to a lower level for my KS3 class.

Involves calculating area and circumference, calculating radius and diameter given area or circumference, and labeling a circle.
By scorpiosami

Area and circumference of circles, semicircles and compound shapes - REVISION SHEET

Revision sheet with questions on circles, semicircles and compound shapes. Answers included.
By cfreely

Areas of Flags (with circles)

A while ago I uploaded a set of resources on calculating the areas of shapes on flags, see here:

A number of people messaged me asking if I had one for circles - and here is is now! I had to get creative with finding flags I could use, and I'd recommend that you have already had a lesson on Area and Circumference before this, as the questions get very challenging!

If you like this resource, then please check out the rest of my stuff!
By Owen134866

Arc length and sectors of a circle

Area of Segments (Grade A/A*) Question Generator

I've made these to send home to parents and also to use in class (either independently or as a whole class).

Nothing special, just generates questions and answers to go with them.

You'll need to enable the macros for this to work.
By arthompson1987

Circles, Arcs, Sectors and Segments

Powerpoint going through questions on. Circle Area and Circumference Leaving in Terms of pi Sectors Arcs Area of any Triangle reminder Segments Exam question combining topics Answers provided in notes. My students had access to this ppt and could work at their own pace/different start points moving onto next ! when comfortable. ! Sign means that something new is happening in this question.
By mhorrocks87

GCSE Arcs, Sectors and Segments - Activities

GCSE geometry starter activities designed for the interactive screen on each of the above topics (complete with answers). Plus as a summary, a nice little game of Catchphrase.
By rhemsley

Surface area of prisms

Surface Area and Volume of Prisms

PPT that goes through how to calculate the surface area and volume of various prisms at a fairly slow pace.
By Daniel Burke

Surface Area Worksheets

Some surface area worksheets. First two sheets have support / structure to help pupils who may be struggling, the last one has no support. Includes cuboids, cylinders and triangular prisms.
By HolyheadSchool

NRICH - Cuboids

3D Shapes, Surface Area
Key Stage: 3 ★★★

Can you find a cuboid that has a surface area of exactly 100 square units? Can you find them all?

This problem requires a lot of calculations of surface areas, within a rich problem solving context.

This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions.

The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.
By nrich_maths

Christmas Eve Panic - Surface Area of Cubes and Cuboids

Putting surface area into some kind of context without using wrapping paper (next best thing here mind). Two worded questions and one which involves two different units of measurement.
By alutwyche

Volume of prisms

Volumes of Prisms - PowerPoint

A PowerPoint document with great annotations. Gives description of how to find the volumes of prisms (cylinders, different shape prisms, cuboids) without memorising the formulae. Although the formula is also given. Gives formulas for areas of genaral shapes along with guided tutorial on how to find general prisms. Ideally used as classroom posters for the whole school or as a tutorial in lessons for KS3 and KS4.
By sneha2009

Sherlocked - Volume (KS3)

Perfect for interactive whiteboards! Allow students to select a question.
By DrFrostMaths

Volume of a Prism (D-B)

A worksheet with answers applying problem solving to prisms
By esoteric1971

Volume of Prisms

Calculate area of end face then volume of prisms. Answers given.
Worksheet 1 has more difficult areas and includes working back from volume.
Worksheet 2 easier cases. Original Promethean flipchart exercise included. Click on Design Mode to reveal answers or edit.
By tumshy

Surface area and volume of non-prisms

GCSE - Volumes and Surface Area of Solids

Covers all aspects of the GCSE curriculum, including algebraic problems where volumes/surface areas are equated. Includes a Powerpoint presentation and a homework. All exercises and answers are within the slides.
By DrFrostMaths

Google Expeditions lesson plan: Aztec and Mayan Ruins

In this lesson, students go on an expedition to some Aztec, Mayan and Inca ruins, focusing on El Castillo in Chichen Itza. The students explain how to work out the perimeter of a composite rectilinear shape. They then draw a diagram of the base of El Castillo and work out the area and volume of each storey, then the total volume of the pyramid.
By TwigWorld

Complex Volumes and Surface Area Homework Pack. (Grades B-A*)

This is a homework pack I have put together for work on complex volumes and surface area. There are sheets for:
- Volume of Pyramids
- Volume and Surface Area of Cones
- Volume and Surface Area of Spheres
These sheets are designed for higher students age 14-16. I have also added in some harder problem solving style questions that are similar to what would be on the new GCSE.
There is also a functional maths activity that could be completed as homework or in class on golf balls. Feedback is deeply appreciated and I'm more than happy to create some answer sheets so just let me know.

Fin :)
By Fin Butler

Volume Problem Solving Questions - Sphere, Cone, Cylinder, Cuboid - Higher Tier A/A*

This is a very challenging task that tests students knowledge of higher tier volume formula

This is a very demanding activity that asks students to solve problems involving 3D shapes.

Task 1 asks students to find the percentage of the container that is filled with water.
Task 2 requires students to visualise the shapes and will test their problem solving faculties, along with their understanding of the volume formulae required.
Task 3 inverts the processes in task 2 and 3 and therefore is little more demanding.
Task 4 is an open ended activity. You can add as much or as little structure to this activity as you like, but some guidelines often allow for a more thorough response from students. Eg. the shape must NOT have constant cross-section.

Some answers provided.

By akcptgrey