Stage 9 - Q1 - 2 marks
A prism has volume 240 cubic cm and cross-section area 24 square cm. Find its length.
Hint
Reverse volume=area×length.
Stage 9 - Q2 - 3 marks
A cylinder has radius 3 cm and volume \(117\pi\) cubic cm. Find its height.
Hint
Use \(h=\frac{V}{\pi r^2}\).
Stage 9 - Q3 - 3 marks
A tank has internal dimensions 10 by 9 by 12 cm. Find its capacity in litres.
Hint
One cubic centimetre holds one millilitre.
Stage 9 - Q4 - 3 marks
A cylinder has height 10 cm and volume \(160\pi\) cubic cm. Find its radius.
Hint
A length is positive.
Stage 9 - Q5 - 3 marks
A straight-sided tank has horizontal cross-section 100 square cm. Add 3 litres of water. How far does the level rise?
Hint
The water forms a prism above its previous level.
Stage 9 - Q6 - 3 marks
A tank has internal dimensions 16 by 12 by 13 cm. Find its capacity in litres.
Hint
One cubic centimetre holds one millilitre.
Stage 9 - Q7 - 4 marks
A cylinder has internal radius 5 cm and height 14 cm. A solid 4 cm cube fits and is fully submerged. Does 1050 mL of water overflow? Ignore wall thickness.
Hint
The fully submerged solid displaces its own volume.
Stage 9 - Q8 - 3 marks
A straight-sided tank has horizontal cross-section 150 square cm. Add 6 litres of water. How far does the level rise?
Hint
The water forms a prism above its previous level.
Stage 9 - Q9 - 4 marks
A cylinder has internal radius 7 cm and height 10 cm. A solid 4 cm cube fits and is fully submerged. Does 1450 mL of water overflow? Ignore wall thickness.
Hint
The fully submerged solid displaces its own volume.
Stage 9 - Q10 - 6 marks
An open cylinder has internal radius 5 cm and height 10 cm. It contains 600 mL of water. A solid cube of side 6 cm is placed flat on the bottom and fully submerged. Does water spill? Find the spilled volume to 1 decimal place.
Hint
A fully submerged solid displaces its own volume. Use 1 mL = 1 cm³.