Chapter 19: Perimeter, area, surface area and volume
The chapter problem: a circular pond path
A circular pond has radius m. A path will run around its edge. First, estimate the distance around the pond and the area of water inside it. You can make a rough prediction now; you will calculate exact values later.
If you are not sure where to start
A circle's distance around it is a little more than three diameters. Its area is a little more than three times the square of its radius.
By the end of this chapter you will be able to:
- calculate perimeters and areas of 2D shapes;
- find circumference, circle area, arc length and sector area;
- calculate surface area and volume of common prisms and curved solids;
- split composite shapes and solids into known parts.
Where the maths can appear
A garden border needs a perimeter measurement. Covering a floor needs an area, and a container's capacity relates to its volume.
Your turn to connect it
Where might you or someone you know need to measure a boundary, cover a surface, or find how much a container holds? Write one example and name the measurement that matters.
Roadmap
- 19.1 Perimeter and area of 2D shapes
- 19.2 Circumference and area of circles
- 19.3 Arc length and sector area
- 19.4 Surface area and volume of prisms and cylinders
- 19.5 Surface area and volume of spheres, cones and pyramids
- 19.6 Composite shapes and solids
- Review
Each section has Learn, Practise with help, and Practise pages. The Review returns to the pond and mixes methods from this chapter with earlier number and ratio skills.