Stage 8 - Q1 - 2 marks
Find the area of a triangular cross-section with base 6 cm and height 4 cm.
Hint
A triangle is half the matching rectangle.
Stage 8 - Q2 - 2 marks
A prism has cross-sectional area 15 cm² and length 8 cm. Find its volume.
Hint
Multiply area by length.
Stage 8 - Q3 - 2 marks
A triangular prism has cross-section base 8 cm, height 3 cm and length 10 cm. Find its volume.
Hint
Keep the triangular factor of one half.
Stage 8 - Q4 - 2 marks
A triangular prism has volume 180 cm³ and cross-sectional area 20 cm². Find its length.
Hint
Reverse multiplication by the area.
Stage 8 - Q5 - 3 marks
A triangular prism has base 5 cm, triangle height 8 cm and volume 260 cm³. Find the prism length.
Hint
The area must be found before dividing the volume.
Stage 8 - Q6 - 3 marks
A triangular prism tank holds 360 cm³ when full. Find the water volume when it is five sixths full, in millilitres.
Hint
The fraction describes volume.
Stage 8 - Q7 - 4 marks
A prism’s triangular base and height both double while its length stays fixed. Compare the new volume with the old.
Hint
Track each dimension that changes.
Stage 8 - Q8 - 4 marks
A solid consists of two identical triangular prisms, each with base 4 cm, height 6 cm and length 9 cm. They are joined along a face with no overlap. Find the total volume.
Hint
Shared surfaces affect surface area, not the sum of volumes.
Stage 8 - Q9 - 5 marks
A triangular prism has volume 240 cm³, cross-section base 8 cm and length 12 cm. A pupil claims the triangle height is 5 cm. Verify the claim independently.
Hint
Use reverse calculation and substitution as two checks.
Stage 8 - Q10 - 6 marks
A triangular prism has base 18 mm, perpendicular triangle height 10 mm and length 24 mm. It is melted into cubes of side 6 mm with no loss. Can eleven complete cubes be made? Find the maximum and justify it.
Hint
Keep all measurements in millimetres and compare volumes, not surface areas.