# Area and Volume

## In this topic you will learn about:

1. Percentage error
2. Area of composite shapes
3. Circular shapes
4. Simpson's rule
5. Volume and surface area of a prism
6. Volume and surface area of a cylinder
7. Volume and surface area of a sphere
8. Volume of pyramids and cones
9. Volume and surface area of composite solids
10. 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