2 Further applications of area and volume Cambridge

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

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

Area of composite shapes q. A composite shape is made up of more than one simple shape. q 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 3 G K Powers 2013

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 4 G K Powers 2013

Surface area of right prisms 1. 2. 3. 4. 5. 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 5 G K Powers 2013

Surface area of cylinders and spheres Open cylinder Curved surface only Area of the top Closed cylinder 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 6 G K Powers 2013

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 7 G K Powers 2013

Volume of composite solids 1. Divide the composite solid into two or more common solids. 2. Calculate the volume of each solid. 3. Add or subtract the volumes of the common solids. 4. 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 8 G K Powers 2013

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