# 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