Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Volume of cylinders, cones and spheres
Geometry
CCSS 8.G.C.9England: GCSE Foundation GeometryEngland: GCSE Higher Geometry
Objective and success criteria
Students will: Volume of cylinders, cones and spheres.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Area of a circle; Volume of prisms
Leads to: Find the volume of composite solids; Find surface areas of cones, spheres and hemispheres
Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Area of a circle; Volume of prisms). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A triangular prism has a triangular end with base 12 ft and height 12 ft. The prism is 3 ft long. What is its volume, in ft³? → 216Prompt: Volume of a prism = area of cross-section × length.
- A circle has diameter 16 m. Its area is kπ m². What is k? → 64Prompt: Find the radius first: half the diameter.
- A triangular prism has a triangular end with base 7 cm and height 2 cm. The prism is 14 cm long. What is its volume, in cm³? → 98Prompt: Volume of a prism = area of cross-section × length.
Hook · 5 min
- Show a photo of a building, a tile pattern or a road sign and ask what shapes and angles students can spot.
- Share the objective: Volume of cylinders, cones and spheres. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: A cylinder has radius 8 yd and height 8 yd. Find its volume in yd³, rounded to 1 decimal place.
- Step 1: π × 8² × 8 = 512π
- Step 2: ≈ 1608.5 yd³
- Answer: 1608.5
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- A cylinder has radius 7 ft and height 11 ft. Find its volume in ft³, rounded to 1 decimal place. → 1693.3Prompt: V = πr²h.
- A cone has radius 7 cm and height 9 cm. Its volume is kπ cm³. What is k? → 147Prompt: V = ⅓πr²h.
You do: independent practice · 10 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A cone has radius 8 cm and height 18 cm. Its volume is kπ cm³. What is k? → 384Prompt: V = ⅓πr²h.
- A sphere has radius 3 ft. Its volume is kπ ft³. What is k? → 36Prompt: V = (4/3)πr³.
Watch out for
- Thinking a square turned on its corner is no longer a square.
- Reading the wrong scale on a protractor.
Support and stretch
Support
- Review first: Area of a circle.
- Use concrete materials: rulers and protractors.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Move on to: Find the volume of composite solids; Find surface areas of cones, spheres and hemispheres.
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-8.
Free lesson plan from eurekami.com/lesson-plan-builder