Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Find the volume of composite solids
Geometry
CCSS HSG.GMD.A.3CCSS HSG.MG.A.1England: GCSE Higher Geometry
Objective and success criteria
Students will: Find the volume of composite solids.
- 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 cylinders, cones and spheres
Leads to: Find the volume of a frustum
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 (Volume of cylinders, cones and spheres). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A cylinder has radius 8 cm and height 11 cm. Find its volume in cm³, rounded to 1 decimal place. → 2211.7Prompt: V = πr²h.
- A cone has radius 8 cm and height 6 cm. Its volume is kπ cm³. What is k? → 128Prompt: V = ⅓πr²h.
- A sphere has radius 6 yd. Its volume is kπ yd³. What is k? → 288Prompt: V = (4/3)πr³.
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: Find the volume of composite solids. 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 rocket model is a cylinder (radius 5 cm, height 9 cm) with a cone (same radius, height 9 cm) on top. Find its volume to 1 decimal place.
- Step 1: π × 5² × 9 ≈ 706.86
- Step 2: ⅓ × π × 5² × 9 ≈ 235.62
- Step 3: ≈ 942.5 cm³
- Answer: 942.5
- 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 rocket model is a cylinder (radius 2 cm, height 7 cm) with a cone (same radius, height 3 cm) on top. Find its volume to 1 decimal place. → 100.5Prompt: Find each part's volume and add them.
- A capsule is a cylinder of radius 6 cm and length 7 cm with a hemisphere on one end. Find its volume to 1 decimal place. → 1244.1Prompt: A hemisphere is half a sphere: ⅔πr³.
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 with the same base and height is drilled out of a solid cylinder (radius 8 cm, height 13 cm). Give the exact remaining volume as a multiple of π. → 554.6666666666666*piPrompt: A cone is one third of the cylinder with the same base and height.
- A rocket model is a cylinder (radius 5 cm, height 4 cm) with a cone (same radius, height 10 cm) on top. Find its volume to 1 decimal place. → 576Prompt: Find each part's volume and add them.
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 cylinders, cones and spheres.
- 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 a frustum.
- 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-10.
Free lesson plan from eurekami.com/lesson-plan-builder