Year 10 Maths • AC9M10M01 • Authored homework
Composite surface area and volume
Solve problems involving surface area and volume of composite solids by decomposing shapes, selecting suitable formulae and interpreting units in context. Show working, use correct units and check reasonableness.
Part A
Short-answer questions
State the difference between surface area and volume.
Find the volume of a rectangular prism measuring 5 cm by 4 cm by 3 cm.
Find the surface area of a cube with side length 6 cm.
Write the formula for the volume of a cylinder.
Write the formula for the curved surface area of a cylinder.
Explain why hidden internal faces are not counted in exposed surface area.
A cylinder has radius 3 cm and height 10 cm. Write, but do not evaluate, its volume expression.
Convert 2.5 L to cubic centimetres.
Name one common unit error in volume problems.
Give one real situation involving composite volume.
Part B
Long-answer questions
A solid is made from two rectangular prisms: 8 cm by 5 cm by 4 cm and 4 cm by 5 cm by 3 cm. Find the total volume.
A cylinder of radius 4 cm and height 12 cm is attached to a hemisphere of radius 4 cm. Write an expression for the total volume.
A shipping box is 40 cm by 30 cm by 25 cm. Find its surface area and explain which faces are counted.
A water tank is a rectangular prism with a half-cylinder top. Describe how you would calculate its capacity.
A composite solid has overlapping faces where two prisms join. Explain how to avoid double-counting surface area.
Find the amount of paint needed to cover the outside of a cuboid shed, excluding the base, if the coverage is 1 L per 8 m^2.
A student uses square centimetres for volume. Explain the error and correct the units.
Design a composite object using at least two simple solids and calculate its volume.
Compare two packages with the same volume but different surface areas and explain why packaging material changes.
Solve a full practical problem involving a composite solid, including diagram description, formulae, calculation, units and interpretation.
Part C
Research and understanding task
Find or design a real composite object, such as a tank, playground shape, package, building feature or container. Break it into simple solids, calculate approximate volume and surface area, and explain assumptions.