0580/32 May/Jun 2023, Question 5: Composite Perimeter, Area and Volume
Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 11 marks
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The question, in short
Use a rectangle with area 12 cm² and perimeter 16 cm to find the area and perimeter of a six-rectangle T-shape, then find a triangle's area, a circle's radius from circumference 28 cm, and a cube's surface area from volume 125 m³.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 4 marks
Find the area and perimeter of the T-shape built from six rectangles, given each rectangle has area 12 cm² and perimeter 16 cm.
- 1Rectangle: length × width = 12 and length + width = 16 ÷ 2 = 8, so 6 cm by 2 cm
- 2Area = 6 × 12 = 72 cm²
- 3Perimeter uses 6 long sides and 8 short sides: 6 × 6 + 8 × 2
- 4= 36 + 16 = 52 cm
- 5Area = 72 cm², Perimeter = 52 cm
AnswerArea = 72 cm², Perimeter = 52 cm
Part (b) · 2 marks
Calculate the area of the triangle with base 16 cm, sloping side 11.7 cm and perpendicular height 8.4 cm.
- 1Area = 1/2 × base × height
- 2= 1/2 × 16 × 8.4 = 67.2 cm²
Answer67.2
Part (c) · 2 marks
Work out the radius of a circle whose circumference is 28 cm.
- 12πr = 28
- 2r = 28 ÷ 2π = 4.456…
- 3≈ 4.46 cm
Answer4.46
Part (d) · 3 marks
Work out the surface area of a cube with volume 125 m³.
- 1Side = ∛125 = 5 m
- 2Area of one face = 5² = 25 m²
- 3Surface area = 6 × 25 = 150 m²
Answer150
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