Math lesson plan · 8th grade (Year 9 in England) · 30 minutes
Find a missing radius or height from a volume
Geometry
CCSS 8.G.C.9CCSS 8.EE.A.2England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Objective and success criteria
Students will: Find a missing radius or height from a volume.
- 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: Volume of a cylinder; Volume of a cone; Solve x² = p and x³ = p
Leads to: the next skill in this area.
Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Volume of a cylinder; Volume of a cone; Solve x² = p and x³ = p). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A cylinder has radius 2 cm and height 8 cm. Find its volume in cm³, to 1 decimal place. → 100.5Prompt: A cylinder is a prism with a circular cross-section.
- A cone has radius 7 cm and height 12 cm. Its volume is kπ cm³. What is k? → 196Prompt: V = ⅓πr²h.
- Solve x² = 196. Give both solutions, separated by a comma. → x = -14 or x = 14Prompt: Which numbers square to give this?
Hook · 3 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: Find a missing radius or height from a volume. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: A cylinder has volume 117π cm³ and radius 3 cm. What is its height, in cm?
- Step 1: 117π ÷ (9π) = 13 cm
- Answer: 13
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 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 volume 325π cm³ and radius 5 cm. What is its height, in cm? → 13Prompt: V = πr²h, so h = V ÷ (πr²).
- A cylinder has volume 28π m³ and height 7 m. What is its radius, in m? → 2Prompt: Divide the volume by πh to get r².
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A cylinder has volume 16π m³ and height 4 m. What is its radius, in m? → 2Prompt: Divide the volume by πh to get r².
- A sphere has volume 2304π cm³. What is its radius, in cm? → 12Prompt: ⁴⁄₃r³ = the number in front of π.
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: Volume of a cylinder.
- 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
- 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