1. 2. Further applications of area and volume
Cambridge University Press
 G K Powers 2013
Study guide Chapter 2

2. Area of circles, annuluses and sectors
Semicircle
Quadrant
HSC Hint – Start area questions by writing the formula or the substitution into the formula.
Cambridge University Press
 G K Powers 2013

3. Area of composite shapes
A composite shape is made up of more than one simple shape.
Area of composite shapes can be found by adding or subtracting the areas of the simple shapes.
Divide this shape into a square and a semicircle. Add the two areas.
HSC Hint – On the diagram, divide the composite area into plane shapes. Mark the measurements that are needed for you to use the appropriate formula.
Cambridge University Press
 G K Powers 2013

4. Simpson’s rule A – Area of the shape
h – Height or width of the equal parts
df – Distance of the first line
dm – Distance of the middle line
dl – Distance of the last line
HSC Hint – Height or width (h) is not the total width. It is only the width of the equal parts.
Cambridge University Press
 G K Powers 2013

5. Surface area of right prisms
Visualise the surfaces of the solid.
Write the formula for the surface area.
Substitute the values into the formula for the surface area.
Use the calculator to find the surface area.
Write the answer to the specified level of accuracy.
HSC Hint – Surface area of a cube:
Surface area of a rectangular prism:
Cambridge University Press
 G K Powers 2013

6. Surface area of cylinders and spheres
Open cylinder
Curved surface only
Closed cylinder
Area of the top
Area of the bottom
Curved surface
Sphere
HSC Hint – Read the question carefully to determine if the cylinder is closed or open.
Cambridge University Press
 G K Powers 2013

7. Volume of pyramids and cones
Square pyramid
Rectangular pyramid
Triangular pyramid
Cone
HSC Hint – Volume of all pyramids and cones use the same formula but with a different base.
Cambridge University Press
 G K Powers 2013

8. Volume of composite solids
Divide the composite solid into two or more common solids.
Calculate the volume of each solid.
Add or subtract the volumes of the common solids.
Write the answer to the specified level of accuracy with correct units.
HSC Hint – The formula sheet contains formulas for the volume of a cone, a cylinder, a pyramid and a sphere. Start a volume question by writing the appropriate formula from that sheet.
Cambridge University Press
 G K Powers 2013

9. Errors in measurement
Limit of reading ‒ smallest unit on the measuring instrument.
Absolute error ‒ ½ × limit of reading (maximum value)
Relative error
Percentage error
HSC Hint – Absolute error is the difference between the actual value and measured value.
Cambridge University Press
 G K Powers 2013