Volume

Volume | NSW Curriculum Website

MA4-VOL-C-01 applies knowledge of volume and capacity to solve problems involving right prisms and cylinders

📖 Prior Knowledge

Content	Prior knowledge	Used for
Three-dimensional Spatial Structure A	- sketching 3D objects in 2D	- sketching different views of prisms and prism combinations
Three-dimensional Spatial Structure B	- volume as multiplying base layers	- establishing volume formula for prisms
Indices	- cubing and cube roots	- volume calculations
Equations	- using formulas	- volume of a prism
Area	- area of plane shapes	- calculating base area for volume

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 the formula for the volume of a prism: $V = B a se a r e a \times h e i g h t$ , leading to $V = A h$
Apply the formula for the volume of a prism to prisms with uniform cross-sections to solve problems

Develop and apply the formula to solve problems involving the volume of cylinders: $V = π r^{2} h$ , where $r$ is the length of the radius of the base and ℎ is the perpendicular height

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 ( $1 cm^{3} = 1000 mm^{3}$ , $1 cm^{3} = 1 mL$ , $1 m^{3} = 1000 L = 1 kL$ , $1000 kL = 1 ML$ )
Solve practical problems involving the volume and capacity of right prisms and cylinders