Circles: circumference and area Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Circles: circumference and area questions. See exactly how to solve problems on circumference of a circle, C = 2 pi r, answer in terms of pi, exact value.

circumference of a circleC = 2 pi ranswer in terms of piexact valuearea of a circleA = pi r squared
GCSE Foundation70 questionsStep-by-step solutions
Question 1
2 markseasy
A circle has radius 55 cm. Work out the circumference of the circle. Give your answer in terms of π\pi.

Worked solution

  1. Write down the formula for the circumference of a circle.

    C=2πr=πdC = 2\pi r = \pi d

    The circumference is 2πr2\pi r, where rr is the radius. The diameter is d=2rd = 2r, so this is the same as πd\pi d.

  2. Substitute the radius into the formula.

    C=2×π×5C = 2 \times \pi \times 5

    The radius is 55, so C=2π×5C = 2\pi \times 5.

  3. State the circumference.

    C=10π cmC = 10\pi\text{ cm}

    The circumference is 10π cm10\pi\text{ cm}.

Answer
C=10π cmC = 10\pi\text{ cm}
Question 2
2 markseasy
A circle has radius 77 cm. Work out the circumference of the circle. Give your answer in terms of π\pi.

Worked solution

  1. Write down the formula for the circumference of a circle.

    C=2πr=πdC = 2\pi r = \pi d

    The circumference is 2πr2\pi r, where rr is the radius. The diameter is d=2rd = 2r, so this is the same as πd\pi d.

  2. Substitute the radius into the formula.

    C=2×π×7C = 2 \times \pi \times 7

    The radius is 77, so C=2π×7C = 2\pi \times 7.

  3. State the circumference.

    C=14π cmC = 14\pi\text{ cm}

    The circumference is 14π cm14\pi\text{ cm}.

Answer
C=14π cmC = 14\pi\text{ cm}
Question 3
1 markeasy
A circle has diameter 99 cm. Work out the circumference of the circle. Give your answer in terms of π\pi.

Worked solution

  1. Write down the formula for the circumference of a circle.

    C=2πr=πdC = 2\pi r = \pi d

    The circumference is 2πr2\pi r, where rr is the radius. The diameter is d=2rd = 2r, so this is the same as πd\pi d.

  2. Substitute the diameter into the formula.

    C=π×9C = \pi \times 9

    The diameter is 99, so C=πd=π×9C = \pi d = \pi \times 9.

  3. State the circumference.

    C=9π cmC = 9\pi\text{ cm}

    The circumference is 9π cm9\pi\text{ cm}.

Answer
C=9π cmC = 9\pi\text{ cm}
Question 4
2 markseasy
A circle has diameter 2020 cm. Work out the circumference of the circle. Give your answer in terms of π\pi.

Worked solution

  1. Write down the formula for the circumference of a circle.

    C=2πr=πdC = 2\pi r = \pi d

    The circumference is 2πr2\pi r, where rr is the radius. The diameter is d=2rd = 2r, so this is the same as πd\pi d.

  2. Substitute the diameter into the formula.

    C=π×20C = \pi \times 20

    The diameter is 2020, so C=πd=π×20C = \pi d = \pi \times 20.

  3. State the circumference.

    C=20π cmC = 20\pi\text{ cm}

    The circumference is 20π cm20\pi\text{ cm}.

Answer
C=20π cmC = 20\pi\text{ cm}
Question 5
2 markseasy
A circle has radius 33 cm. Work out the area of the circle. Give your answer in terms of π\pi.

Worked solution

  1. Write down the formula for the area of a circle.

    A=πr2A = \pi r^2

    The area of a circle of radius rr is πr2\pi r^2. Only the radius is squared — π\pi is not.

  2. Substitute the radius and square it.

    A=π×32=9πA = \pi \times 3^2 = 9\pi

    32=93^2 = 9, so A=9πA = 9\pi.

  3. State the area.

    A=9π cm2A = 9\pi\text{ cm}^2

    The area is 9π cm29\pi\text{ cm}^2.

Answer
A=9π cm2A = 9\pi\text{ cm}^2

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