4024/21 Oct/Nov 2023, Question 9: Surface Area of a Cuboid and Cylinder
Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 14 marks
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The question, in short
Triangular prism with AB = 6 cm, angle BAC = 55°, length 20 cm, triangle area 34.4 cm²; cuboid with square base, height 8 cm, volume 98 cm³; find volume, AC, surface area, and PQ.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (ai) · 2 marks
Calculate the volume of the prism using its cross-sectional area and length, and state the units.
- 1Volume = 34.4 × 20
- 2= 688 cm³
Answer688 cm³
Part (aii) · 3 marks
Show that AC = 14.0 cm to 3 significant figures, using the triangle area and given values.
- 11/2 × 6 × AC × sin 55° = 34.4
- 2AC = 68.8 ÷ (6 × sin 55°)
- 3= 13.998… = 14.0 cm (3 s.f.)
Answer13.998[…] or 14.00
Part (aiii) · 5 marks
Calculate the total surface area of the triangular prism.
- 1BC² = 6² + 14² − 2 × 6 × 14 × cos 55° = 135.63…
- 2BC = 11.64…
- 3Surface area = 2 × 34.4 + 6 × 20 + 14 × 20 + 11.64… × 20
- 4= 68.8 + 120 + 280 + 232.9… = 701.7… ≈ 702 cm²
Answer702 or 701.6 to 701.8
Part (b) · 4 marks
Calculate the length PQ, the space diagonal between opposite corners of the cuboid.
- 1Area of base = 98 ÷ 8 = 12.25, so side = 3.5 cm
- 2PQ² = 3.5² + 3.5² + 8² = 12.25 + 12.25 + 64 = 88.5
- 3PQ = √88.5 = 9.407… ≈ 9.41 cm
Answer9.41 or 9.407…
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