Ch 15 Working in 3D Lesson
Volume and Surface Area of 3D Solids
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Year 11 (KS4)BTC Style / Thinking Classrooms50 min
Learning Objective
Students will calculate volume and surface area of prisms, cylinders, cones, pyramids, spheres, and composite solids, and solve reverse problems involving these measures.
Lesson Overview
Students progress from calculating volume and surface area of simple prisms and cylinders through to composite solids and reverse problems, changing one variable at a time across 12 thin-sliced tasks.
Materials
- Whiteboard or vertical surface and markers
- Pencil and paper
- Calculator (phone calculator is fine)
Scaffolded Task Progression
1Task 1
A rectangular prism (cuboid) has length $8$ cm, width $5$ cm, and height $3$ cm.
```solid
{"figureType":"solid","solid":"rectPrism","length":8,"width":5,"height":3,"labels":{"length":"8 cm","width":"5 cm","height":"3 cm"},"title":"Rectangular Prism"}
```
(a) Find the volume.
(b) Find the total surface area.
2Task 2
A rectangular prism has length $10$ cm, width $4$ cm, and height $6$ cm.
```solid
{"figureType":"solid","solid":"rectPrism","length":10,"width":4,"height":6,"labels":{"length":"10 cm","width":"4 cm","height":"6 cm"},"title":"Rectangular Prism"}
```
(a) Find the volume.
(b) Find the total surface area.
3Task 3
A cylinder has radius $r = 4$ cm and height $h = 10$ cm.
```solid
{"figureType":"solid","solid":"cylinder","radius":4,"height":10,"labels":{"radius":"4 cm","height":"10 cm"},"title":"Cylinder"}
```
(a) Find the volume. Leave your answer in terms of $\pi$.
(b) Find the total surface area. Leave your answer in terms of $\pi$.
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