Area and Volume
Chapter Three
In this topic you will learn about:
- Percentage error
- Area of composite shapes
- Circular shapes
- Simpson's rule
- Volume and surface area of a prism
- Volume and surface area of a cylinder
- Volume and surface area of a sphere
- Volume of pyramids and cones
- Volume and surface area of composite solids
- Error in area and volume calculations
This smore discusses the first eight of these points. The bottom two are applications of the above.
1. Percentage error
Any measurement has accuracy equal to +/- the smallest unit marked on the scale of a measuring device. This accuracy is called the absolute error.
Read this explanation of how to calculate the percentage error
Error and Percent Error
2. Composite shapes
The following formulas are on your formula sheet. You need to know how to use them:
- Circle
- Sector
- Annulus
- Trapezium
You also need to know how to work out:
- Area of a rectangle
- Area of a triangle
- Area of parallelogram
- Area of a rhombus
Don't forget Pythagoras' Theorem. You will use it to solve some of these problems.
3. Circular shapes
You need to know how to use the following formulae:
- Length of an arc. An arc is a part of the circumference a circle. Its length is a fraction of a circle. There are 360 degrees in a circle.
- Area of a sector. A sector is a region of a circle bounded by an arc and two radii. Its area is a fraction of the circle.
These two formulae can be found on your formula sheet
4. Simpson's Rule
Simpson's Rule is a method for approximating the area of irregular shapes.
From the HSC Data Sheet:
Simpsons Rule (Term 2 HSC general pg22)
5. Volume and surface area of a prism
Volume of a prism = Area of base x Perpendicular Height
The surface area of a solid is the amount of area that covers all its faces.
6. Volume and Surface Area of a cylinder.
The Volume of a cylinder is calculated the same way as for a prism:
Volume = Area of base (a circle) x Height
The formula for surface area of a cylinder is on the HSC data sheet
how to find the surface area of a cylinder
7. Volume and surface area of a sphere
You need to be able to calculate and work with both the volume and surface area of a sphere. The surface area formula is on the HSC data sheet, and a video for volume is linked below.
Volume of a sphere | Perimeter, area, and volume | Geometry | Khan Academy
8. Volumes of pyramids and cones
The volume of a pyramid (or cone) is one third of the volume of a prism of the same base and height. The volume formula is contained on the HSC data sheet.
Volume of a cone | Perimeter, area, and volume | Geometry | Khan Academy