Math lesson plan · 10th grade (Year 11 in England) · 30 minutes
Find surface areas of cones, spheres and hemispheres
Geometry
CCSS HSG.GMD.A.3England: GCSE Higher Geometry
Objective and success criteria
Students will: Find surface areas of cones, spheres and hemispheres.
- 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; Pythagoras' theorem
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 cylinders, cones and spheres; Pythagoras' theorem). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A cylinder has radius 6 ft and height 6 ft. Find its volume in ft³, rounded to 1 decimal place. → 678.6Prompt: V = πr²h.
- A cone has radius 5 ft and height 15 ft. Its volume is kπ ft³. What is k? → 125Prompt: V = ⅓πr²h.
- A cylinder has radius 6 yd and height 12 yd. Find its volume in yd³, rounded to 1 decimal place. → 1357.2Prompt: V = πr²h.
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 surface areas of cones, spheres and hemispheres. 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: Find the surface area of a sphere of radius 12 cm. Give an exact answer in terms of π.
- Step 1: 4 × π × 12² = 576π cm²
- Answer: 576*pi
- 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.
- Find the surface area of a sphere of radius 7 cm. Give an exact answer in terms of π. → 196*piPrompt: Surface area of a sphere = 4πr².
- A cone has base radius 5 cm and perpendicular height 12 cm. Find its curved surface area, in terms of π. → 65*piPrompt: First find the slant height l with Pythagoras.
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.
- Find the total surface area of a solid hemisphere of radius 5 cm (curved part and flat face). Give it in terms of π. → 75*piPrompt: The curved part is half of 4πr².
- A cone has base radius 16 cm and perpendicular height 30 cm. Find its total surface area, in terms of π. → 800*piPrompt: First find the slant height l with Pythagoras.
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
- 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