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0580/41 May/Jun 2023, Question 4: Composite Perimeter, Area and Volume

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 14 marks

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The question, in short

Using the given diagrams, find the area of triangle PQR, angle PRQ, the volume of a half-cylinder, and the area and perimeter of a shaded shape left after removing DSXT from rectangle ABCD.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 2 marks

Calculate the area of triangle PQR using PQ = 8 cm and QR = 24 cm.

  1. 1Area = 1/2 × 24 × 8 = 96 cm²

Answer96

Part (aii) · 2 marks

Calculate angle PRQ in the right-angled triangle PQR.

  1. 1tan PRQ = 8/24
  2. 2Angle PRQ = tan⁻¹(8/24) = 18.43…° ≈ 18.4°

Answer18.4 or 18.43...

Part (b) · 2 marks

Calculate the volume of a half-cylinder with radius 6 cm and length 11 cm.

  1. 1Volume = 1/2 × π × 6² × 11
  2. 2= 198π = 622.0… ≈ 622 cm³

Answer622 or 622.0 to 622.1....

Part (ci) · 5 marks

Calculate the area of the shaded shape left after removing DSXT from rectangle ABCD, with AB = 20 cm, BC = 15 cm, circle radius 4 cm.

  1. 1Rectangle = 15 × 20 = 300 cm²
  2. 2Removed shape = square DSOT + 3/4 of the circle
  3. 3Square DSOT = 4 × 4 = 16 cm²
  4. 43/4 of circle = 270/360 × π × 4² = 12π = 37.69… cm²
  5. 5Shaded area = 300 − 16 − 37.69… = 246.3… ≈ 246 cm²

Answer246 or 246.2 to 246.3...

Part (cii) · 3 marks

Calculate the perimeter of the shaded shape.

  1. 1Straight edges = 15 + 20 + (15 − 4) + (20 − 4) = 15 + 20 + 11 + 16 = 62 cm
  2. 2Arc = 3/4 × 2 × π × 4 = 6π = 18.84… cm
  3. 3Perimeter = 62 + 18.84… = 80.84… ≈ 80.8 cm

Answer80.8 or 80.9 or 80.84 to 80.85...

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Also searched as: 0580/41/M/J/23 · 0580_s23_qp_41 · 0580 s23 41 · question 4.
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