Perimeter, area and volume - intermediate

This lesson comprises two (2) master classes focusing on:

• Area of special quadrilaterals
• Area of circles and sectors
• Surface area of prisms and cylinders
• Surface area of composite solids
• Volume of prisms and cylinders
• Volume of composite solids

Content:

MA4-ARE-C-01

Develop and use formulas to find the area of rectangles, triangles and parallelograms to solve problems

• Apply the formula to find the area of a rectangle or square: \( A=lb \) , where \( l \) is the length and \( b \) is the breadth (or width) of the rectangle or square
• Develop and apply the formula to find the area of a triangle: \( A=\frac{1}{2}bh \), where \( b \) is the base length and \( h \) is the perpendicular height
• Develop and apply the formula to find the area of a parallelogram:  \( A=bh \) where \( b \) is the base length and \( h \) is the perpendicular height
• Calculate the area of composite figures that can be dissected into rectangles, squares, parallelograms or triangles to solve problems

Develop and use the formula to find the area of circles and sectors to solve problems

• Develop and apply the formula to find the area of a circle: \( A=\pi r^2 \) where \( r \) is the length of the radius
• Explain how the area of a sector can be developed from the area of a circle \( A=\frac{\theta}{360^\circ} \times \pi r^2 \)
• Find the area of quadrants, semicircles and sectors, and apply these formulas in the context of real-life problems
• Calculate the areas of composite shapes involving quadrants, semicircles and sectors to solve problems

Develop and use the formulas to find the area of trapeziums, rhombuses and kites to solve problems

• Develop and apply the formula to find the area of a kite or rhombus: \( A=\frac{1}{2}xy \) where \( x \) and \( y \) are the lengths of the diagonals
• Develop and apply the formula to find the area of a trapezium: \( A=\frac{h}{2}(a+b) \) where \( h \) is the perpendicular height and \( a \) and \( b \) are the lengths of parallel sides
• Calculate the area of composite shapes involving trapeziums, kites and rhombuses to solve problems

Choose appropriate units of measurement for area and convert between units

• Choose an appropriate unit to measure the area of different shapes and surfaces and justify the choice
• Convert between metric units of area using \( 1 cm^2=100 mm^2 \), \( 1 m^2=10 000 cm^2 \), \( 1 ha=10 000 m^2 \) and \( 1 km^2=1 000 000 m^2=100 ha \).

MA5-ARE-C-01

Solve problems involving areas and surface areas

• Solve practical problems involving the areas of composite shapes
• Identify the edge lengths and the faces making up the surface area of prisms
• Recognise and justify whether a diagram represents a net of a right prism
• Create and rearrange nets of right prisms
• Find the surface areas of prisms, given their nets, excluding curved surfaces
• Solve problems involving surface areas of prisms, excluding curved surfaces

Develop and apply the formula for surface areas of cylinders

• Recognise the curved surface of a cylinder as a rectangle and apply this knowledge to calculate the area of the curved surface
• Develop and apply the formula to find the surface area of a closed cylinder: \( A=2 \pi r+2 \pi rh \) where \( r \) is the length of the radius and \( h \) is the perpendicular height

Solve problems involving surface areas of cylinders and related composite solids

• Solve problems involving surface areas of cylinders and related composite solids

MA4-VOL-C-01

Describe the different views of prisms and solids that have been formed from prism combinations

• Represent prisms from different views in 2 dimensions, including top, side, front and back views
• Describe and illustrate solids formed from prism combinations from different views in 2 dimensions, including top, side, front and back views
• Identify and illustrate the cross-sections of different prisms
• Examine the idea that prisms have a uniform cross-section that is equal to the base area
• Determine if a particular solid has a uniform cross-section

Develop and apply the formula to find the volume of a prism to solve problems

• Develop the formula for the volume of a prism: \( V= base\ area \times height\), leading to \( V= Ah \)
• Apply the formula for the volume of a prism to prisms with uniform cross-sections to solve problems

Develop the formula for finding the volume of a cylinder and apply the formula to solve problems

• Develop and apply the formula to solve problems involving the volume of cylinders: \( V= \pi r^2h \)
  where \( r \) is the length of the radius of the base and \( h \) is the perpendicular height

Choose appropriate units of measurement for volume and capacity and convert between units

• Recognise that 1000 L is equal to 1 kilolitre (kL) and use the abbreviation
• Recognise that 1000 kL is equal to 1 megalitre (ML) and use the abbreviation
• Choose an appropriate unit to measure the volume or capacity of different objects and justify the choice
• Convert between metric units of volume and capacity (\( 1 cm^3=1000 mm^3\),  \( 1 cm^3=1 mL\), \( 1 m^3=1000 L= 1KL\), \( 1000 KL=1 ML\))
• Solve practical problems involving the volume and capacity of right prisms and cylinders

MA5-VOL-C-01

Solve problems involving composite solids consisting of right prisms and cylinders

• Find the volumes of composite right prisms with uniform cross-sections that may be dissected into triangles and quadrilaterals
• Find the volumes of right prisms that have uniform cross-sections in the form of sectors, semicircles and quadrants
• Calculate volumes of composite solids consisting of right prisms and cylinders
• Solve practical problems related to the volumes and capacities of composite solids