Volume

measurementandspace core

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	Prerequisite relationships
Multiplicative Relations B	- Multiply and divide decimals by powers of 10 → Convert between units of volume and capacity
Two-dimensional Spatial Structure A	- Calculate the area of a rectangle → Find the volume of a prism
Three-dimensional Spatial Structure A	- Compare prisms and pyramids → Identify cross-sections of prisms - Sketch 3D objects from different views → Draw different views of prisms
Three-dimensional Spatial Structure B	- Calculate the volume of a rectangular prism → Find the volume of a prism
Indices	- Evaluate numbers in index notation → Convert between units of volume and capacity
Equations	- Solve equations from formulas → Find a dimension given the volume - Solve quadratics from formulas → Find a dimension given the volume
Area	- Find the area of a circle → Find the volume of a cylinder

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

• 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.pdf

• Develop the formula for the volume of a prism: $V=Basearea\times height$, 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.pdf

• Develop and apply the formula to solve problems involving the volume of cylinders: $V=\pi r^{2}h$, 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.pdf

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