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GCSE Maths · Higher · Chapter 9: Length, area and volume · Lesson 1

Circles and sectors

Grades 4–8About 55 minutesCalculator allowed39 marks
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NameClassDate
A

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

  1. A1
    Needed today

    A rectangle has area cm and width cm. Find its length.

    [1 mark]
    Answer
  2. A2
    From chapter 4

    Find the 10th term of the sequence .

    [1 mark]
    Answer
  3. A3
    From chapter 7

    Describe the locus of points 4 cm from a point .

    [1 mark]
    Answer
  4. A4
    Last lesson

    Make the subject of .

    [1 mark]
    Answer
B

Example, then your turn

Grades 4–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

A round mat has diameter m. Work out its area, to s.f.

Hint Halve the diameter first: the area is .
  1. B1

    A round mat has diameter m. Work out its area, to s.f.

    [2 marks]
    Answer
Example 2

Work out the area of the sector, to s.f.

10 cm72°
Hint The sector is of the whole circle.
  1. B2

    Work out the area of the sector, to s.f.

    [2 marks]
    9 cm160°
    Answer
C

Practice

Grades 5–7
  1. C1

    Work out the perimeter of the semicircle, to s.f.

    [2 marks]
    9 cm
    Answer
  2. C2

    The two circles have the same centre. Work out the area of the shaded ring in terms of .

    [2 marks]
    7 cm4 cm
    Answer
  1. C3

    Work out the perimeter of the sector. Give it in the form .

    [3 marks]
    15 cm48°
    Answer
  2. C4

    The arc of the sector is cm long. Work out the angle of the sector.

    [2 marks]
    18 cm?
    Not drawn accurately
    Answer
  3. C5

    A round pond has area m. Work out its diameter, to s.f.

    [3 marks]
    Answer
  4. C6

    A wheel of diameter cm rolls m. How many complete turns does it make?

    [3 marks]
    Answer
D

Exam-style questions

Grades 6–8
  1. D1

    A small pizza has a diameter of cm and costs £. A large pizza has a diameter of cm and costs £. Amir says, "The large pizza is twice as wide, so it has twice the area. It costs more than three times as much, so it is worse value."

    18 cm£536 cm£16
    (a)

    Show that the large pizza has times the area of the small pizza.

    [2 marks]
    (b)

    Is Amir right that the large pizza is worse value? You must show your working.

    [3 marks]
    Total for D1: 5 marks
  1. D2

    The shaded shape is a semicircle of diameter cm with semicircles of diameter cm and cm cut out along its diameter.

    8 cm6 cm14 cm
    (a)

    Show that the perimeter of the shaded shape is cm.

    [2 marks]
    (b)

    Work out the area of the shaded shape. Give your answer in terms of .

    [3 marks]
    Answer
    (c)

    A circle has the same area as the shaded shape. Work out its circumference, to s.f.

    [2 marks]
    Answer
    Total for D2: 7 marks
E

Extension

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

  1. E1

    A sector of a circle has radius cm. The perimeter of the sector is cm. Work out the area of the sector.

    [4 marks]
    Hint 1 · What to try

    Take the two radii off the perimeter. What is left is the arc.

    Hint 2 · The first line

    The arc is cm out of a whole circumference of cm. That fraction of the circle is the sector.

    Hint 3 · The full method

    Area . The cancels.

    Answer cm
F

How did it go?

Colour one circle on each line.
Not yetNearlyYes
I can work out the circumference and area of a circle, and work back to the radius.
I can work out the arc length, perimeter and area of a sector, and its angle from them.
I can use circles and sectors in problems, giving answers in terms of when asked.

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