[discia] GCSE Maths › Geometry & Measures › Area and Circumference of Circles

Area and Circumference of Circles

discia.org 10 questions · 25 marks
Name Date
  1. Either paper 1 mark
    Rosa adds labels to this diagram of a circle with centre \(O\). ABCDEFO
    LineRosa's label
    \(AB\)radius
    \(OC\)radius
    \(DE\)chord
    the line touching the circle at \(F\)tangent
    Explain why one of the labels is wrong.
    Show answer
    The line \(AB\) is labelled "radius" but it goes all the way across the circle through O; a radius only goes from the centre to the circumference.
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  2. Either paper 2 marks

    Here is a circular pond being made in a garden.

    O2 cm

    The radius of the circle is \(2\) cm.

    Work out the area of the circle. Give your answer in terms of \(\pi\).

    Show answer
    \(4\pi\ \text{cm}^2\)
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  3. Calculator 2 marks
    O11 cm

    The circle has a radius of \(11\) cm.

    Work out its area. Give your answer correct to 1 decimal place.

    Show answer
    \(380.1\ \text{cm}^2\)
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  4. Either paper 2 marks
    ABO

    \(AB\) is a diameter of the circle and \(AB = 10\) cm.

    Calculate the circumference of the circle. Give your answer in terms of \(\pi\).

    Show answer
    \(10\pi\ \text{cm}\)
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  5. Either paper 2 marks
    Or cm

    The circumference of the circle is \(14\pi\) cm.

    Find the radius of the circle.

    Show answer
    \(7\ \text{cm}\)
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  6. Either paper 3 marks
    (a)

    The diagram shows a circle with centre \(O\). \(AB\) is a diameter and \(AB = 22\) cm.

    ABO22 cm

    The shaded region is a semicircle.

    Calculate the perimeter of the shaded semicircle. Give your answer in terms of \(\pi\).

    (b)

    Calculate the area of the shaded semicircle. Give your answer in terms of \(\pi\).

    Show answer
    (a) \((11\pi + 22)\ \text{cm}\)
    (b) \(\frac{121}{2}\pi\ \text{cm}^2\)
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  7. Either paper 3 marks
    (a)

    \(OA\) and \(OB\) are radii of a circle with centre \(O\), and angle \(AOB = 90^\circ\).

    ABO6 cm90°

    \(OA = 6\) cm and the shaded region is a quarter of the circle.

    Work out the length of the arc \(AB\). Give your answer in terms of \(\pi\).

    (b)

    Work out the area of the shaded quarter circle. Give your answer in terms of \(\pi\).

    Show answer
    (a) \(3\pi\ \text{cm}\)
    (b) \(9\pi\ \text{cm}^2\)
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  8. Calculator 3 marks
    (a)

    Priya's bicycle wheel has a diameter of \(50\) cm.

    O50 cm

    Calculate how far the wheel travels in one complete turn. Give your answer correct to 1 decimal place.

    (b)

    Calculate how far the wheel travels in \(40\) complete turns. Give your answer in metres, correct to 1 decimal place.

    Show answer
    (a) \(157.1\ \text{cm}\)
    (b) \(62.8\ \text{m}\)
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  9. Calculator 3 marks

    Here is a circle with radius \(9\) cm.

    9 cm

    Here is a square with side \(14\) cm.

    14 cm

    The shapes are not drawn accurately.

    Which has the greater area, the circle or the square?

    You must show your working.

    Show answer
    The circle: circle \(\approx 254.5\ \text{cm}^2\), square \(196\ \text{cm}^2\)
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  10. Calculator 4 marks

    The plan of a patio is a rectangle with a semicircular pond cut out of one end. The pond is not paved.

    16 m16 m9 m

    The semicircle has the full width of the rectangle as its diameter.

    One pack of paving slabs covers \(116\) m².

    Is this enough to pave the whole patio? You must show your working.

    Show answer
    Yes: area \(\approx 112.19\) m² against \(116\) m²
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discia.org Area and Circumference of Circles · sheet 1
Answers Area and Circumference of Circles · sheet 1
  1. The line \(AB\) is labelled "radius" but it goes all the way across the circle through O; a radius only goes from the centre to the circumference.
  2. \(4\pi\ \text{cm}^2\)
  3. \(380.1\ \text{cm}^2\)
  4. \(10\pi\ \text{cm}\)
  5. \(7\ \text{cm}\)
  6. (a) \((11\pi + 22)\ \text{cm}\)
    (b) \(\frac{121}{2}\pi\ \text{cm}^2\)
  7. (a) \(3\pi\ \text{cm}\)
    (b) \(9\pi\ \text{cm}^2\)
  8. (a) \(157.1\ \text{cm}\)
    (b) \(62.8\ \text{m}\)
  9. The circle: circle \(\approx 254.5\ \text{cm}^2\), square \(196\ \text{cm}^2\)
  10. Yes: area \(\approx 112.19\) m² against \(116\) m²
discia.org Area and Circumference of Circles · sheet 1