Year 9 Maths • AC9M9M01 • Authored homework
Surface area, volume and capacity modelling
Solve problems involving surface area, volume and capacity of right prisms, cylinders and composite solids. Use suitable units and interpret answers in practical contexts. Show working, use correct units or notation, and check reasonableness.
Part A
Short-answer questions
Find the volume of a rectangular prism 8 cm by 5 cm by 3 cm.
Convert 2500 cm^3 to litres.
Find the surface area of a cube with side length 6 cm.
State the formula for the volume of a cylinder.
Find the volume of a cylinder with radius 4 cm and height 10 cm in terms of pi.
Explain the difference between volume and surface area.
A tank has capacity 72 000 cm^3. Convert this to litres.
Name one situation where surface area matters more than volume.
Correct this error: surface area of a rectangular prism is length × width × height.
Estimate whether a 1 L bottle can hold 900 cm^3 of water and explain.
Part B
Long-answer questions
A rectangular aquarium is 60 cm by 30 cm by 40 cm. Find its volume in cm^3 and capacity in litres.
Find the surface area of a closed rectangular box with dimensions 12 cm, 8 cm and 5 cm. Show all faces.
A cylindrical can has radius 3 cm and height 12 cm. Find its volume and total surface area in terms of pi.
A prism is made by joining two rectangular prisms. Explain how to find its total volume without double-counting.
Design packaging for a rectangular product and calculate the cardboard needed, allowing for overlap.
Compare two containers with different dimensions and decide which has greater capacity.
A swimming pool is 8 m long, 4 m wide and 1.5 m deep. Find the volume of water in cubic metres and litres.
Explain why using consistent units is essential in a volume and capacity problem.
Solve a practical problem involving paint, wrapping, filling or storage using surface area or volume.
Write a full modelling response for a container problem, including assumptions, formula, unit conversion and final interpretation.
Part C
Research and understanding task
Measure or estimate a real container, box, room, tank or package. Calculate its volume/capacity and at least one surface area measurement, then explain assumptions and units.