Lemmara logoLemmaraWorked solution

0580/31 Oct/Nov 2022, Question 6: Circumference and Area of a Circle

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 12 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Identify a solid from its picture, use an isosceles triangle on a straight line to get x, find a 15-sided polygon's interior angle, and work with a circle through A, B and C with centre O.

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

Part (a) · 1 mark

State the mathematical name of the pictured solid.

  1. 1The solid has two equal circular ends joined by a curved surface
  2. 2It is a cylinder

AnswerCylinder

Part (b) · 2 marks

Given BE = CE and angle ABE = 104°, determine the size of angle x at E.

  1. 1Angle EBC = 180 − 104 = 76° (angles on a straight line)
  2. 2Angle ECB = 76° (isosceles triangle, BE = CE)
  3. 3x = 180 − 76 − 76 = 28 (angles in a triangle)

Answer28

Part (c) · 2 marks

Calculate one interior angle of a regular 15-sided polygon.

  1. 1Exterior angle = 360 ÷ 15 = 24°
  2. 2Interior angle = 180 − 24 = 156°

Answer156

Part (di) · 1 mark

Give the mathematical name for the line BC in the circle diagram.

  1. 1BC joins two points on the circle and does not pass through the centre
  2. 2BC is a chord

AnswerChord

Part (dii) · 1 mark

Construct a tangent touching the circle at B.

  1. 1Draw a straight line touching the circle only at B
  2. 2It is perpendicular to the radius OB

AnswerTangent drawn at point B

Part (diii) · 3 marks

Using a circle area of 245.5 cm², calculate the length AB, which passes through O.

  1. 1πr² = 245.5
  2. 2r² = 245.5 ÷ π = 78.14...
  3. 3r = 8.839...
  4. 4AB = 2r = 17.67... ≈ 17.7 cm

Answer17.7 or 17.67 to 17.68

Part (div) · 2 marks

With angle BAC = 38°, determine the value of y, the angle at B.

  1. 1AB is a diameter, so angle ACB = 90° (angle in a semicircle)
  2. 2y = 180 − 90 − 38 = 52

Answer52

Stuck on a step? Read the free lesson: Circumference and Area of a Circle

Practise more circumference and area of a circle questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on circumference and area of a circle

Also searched as: 0580/31/O/N/22 · 0580_w22_qp_31 · 0580 w22 31 · question 6.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.