Stage 9 - Q1 - 2 marks
Find the volume of the prism with the labelled cross-section area and length.
Hint
The shaded measurement is already an area.
Stage 9 - Q2 - 3 marks
Find the cylinder volume. Give an exact answer in terms of pi and an approximation to 1 decimal place.
Hint
Halve the diameter if the diagram gives d.
Stage 9 - Q3 - 2 marks
A prism has volume 168 cubic cm and cross-section area 24 square cm. Find its length.
Hint
Reverse volume=area×length.
Stage 9 - Q4 - 4 marks
Find the total surface area of the closed right-triangular prism.
Hint
Surface area includes every external face.
Stage 9 - Q5 - 3 marks
The right square pyramid has base side \(a\) and perpendicular face slant height \(l\). Find its total surface area.
Hint
The slant height is perpendicular within a triangular face.
Stage 9 - Q6 - 3 marks
Find the area of the closed cylinder, radius 7 cm and height 7 cm. Give an exact answer and 1 decimal place.
Hint
Decide how many circular ends are actually present.
Stage 9 - Q7 - 3 marks
A cuboid has three different side lengths 7, 9, 11 cm. State and describe all its planes of symmetry.
Hint
Consider a central cut parallel to each face direction.
Stage 9 - Q8 - 3 marks
A triangular tube has right-triangle sides 15, 20, 25 cm and length 19 cm. Both triangular ends are open. Find the material area.
Hint
List the faces that are actually present.
Stage 9 - Q9 - 3 marks
Find the area of the label covering only the curved side, radius 2 cm and height 15 cm. Give an exact answer and 1 decimal place.
Hint
Decide how many circular ends are actually present.
Stage 9 - Q10 - 7 marks
Choose the least-material open-top container that holds at least 600 mL. Internal dimensions in cm: A cylinder r=4, h=12; B cylinder r=5, h=8; C cuboid 8 by 8 by 10. Ignore thickness and joins; material cost per cm² is the same. Justify the choice.
Hint
Check the capacity condition before comparing areas, and remove the lid from each area calculation.