Circles

12 Grade 8 Mathematics questions on Circles, with worked marking schemes. 12 questions are available on this topic in full.

1. Question 1

   1 mark

   Find the length of an arc subtending 45 degrees in a circle of radius 28 cm. (Take pi = 22/7)

   A. 22 cm

   B. 44 cm

   C. 11 cm

   D. 176 cm

   (1 mark)

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2. Question 2

   4 marks

   A circle has radius 21 cm. (Take pi = 22/7)

   (a) Find the circumference. (2 marks)

   (b) Find the length of an arc that subtends 60 degrees at the centre. (2 marks)

   Marking scheme

   (a) The circumference of a circle is $2\pi r$. With $r=21$ cm and $\pi =\frac{22}{7}$: $2\times \frac{22}{7}\times 21$. (1)

   $\frac{22}{7}\times 21=66$, so the circumference is $2\times 66=132$ cm. (1)

   (b) An arc is the fraction $\frac{60}{360}=\frac{1}{6}$ of the whole circumference. (1)

   So the arc length is $\frac{1}{6}\times 132=22$ cm. (1)

   Final answer: the circumference is $132$ cm and the arc is $22$ cm.

3. Question 3

   3 marks

   A wheel has radius 0.35 m. Taking pi = 22/7, find how many complete revolutions it makes to cover 220 m.

   (3 marks)

   Marking scheme

   One complete revolution moves the wheel forward by its circumference, $2\pi r$. (1)

   With $r=0.35$ m: $2\times \frac{22}{7}\times 0.35=2.2$ m for each revolution. (1)

   Divide the total distance by the distance per revolution: $220÷2.2=100$. (1)

   Final answer: $100$ complete revolutions.

4. Question 4

   1 mark

   The circumference of a circle is 132 cm. Find its diameter. (Take pi = 22/7)

   A. 21 cm

   B. 84 cm

   C. 42 cm

   D. 66 cm

   (1 mark)

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5. Question 5

   1 mark

   Find the circumference of a circle of radius 14 cm. (Take pi = 22/7)

   A. 44 cm

   B. 88 cm

   C. 22 cm

   D. 176 cm

   (1 mark)

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6. Question 6

   3 marks

   The length of an arc of a circle is 44 cm and it subtends an angle of 90 degrees at the centre. Find the radius of the circle. (Take pi = 22/7)

   (3 marks)

   Marking scheme

   An arc is a fraction of the whole circumference, and that fraction is $\frac{\theta }{360}$. So arc $=\frac{\theta }{360}\times 2\pi r$. (1)

   Substitute the arc $44$ cm, $\theta =90^{\circ }$ and $\pi =\frac{22}{7}$: $\frac{90}{360}\times 2\times \frac{22}{7}\times r=44$, which simplifies to $\frac{11}{7}r=44$. (1)

   Multiply both sides by $\frac{7}{11}$: $r=44\times \frac{7}{11}=28$. (1)

   Final answer: $28$ cm.

7. Question 7

   1 mark

   Find the perimeter of a semicircle of radius 7 cm. (Take pi = 22/7)

   A. 22 cm

   B. 44 cm

   C. 36 cm

   D. 29 cm

   (1 mark)

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8. Question 8

   1 mark

   Find the length of an arc that subtends 90 degrees at the centre of a circle of radius 14 cm. (Take pi = 22/7)

   A. 44 cm

   B. 22 cm

   C. 11 cm

   D. 88 cm

   (1 mark)

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9. Question 9

   1 mark

   Find the circumference of a circle of diameter 21 cm. (Take pi = 22/7)

   A. 66 cm

   B. 33 cm

   C. 132 cm

   D. 21 cm

   (1 mark)

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10. Question 10

    1 mark

    Find the circumference of a circle of radius 7 cm. (Take pi = 22/7)

    A. 22 cm

    B. 49 cm

    C. 44 cm

    D. 14 cm

    (1 mark)

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11. Question 11

    1 mark

    A circular running track has radius 35 m. How far does an athlete run in one complete lap? (Take pi = 22/7)

    A. 220 m

    B. 110 m

    C. 1100 m

    D. 70 m

    (1 mark)

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12. Question 12

    1 mark

    The circumference of a circle is 88 cm. Find its radius. (Take pi = 22/7)

    A. 28 cm

    B. 44 cm

    C. 7 cm

    D. 14 cm

    (1 mark)

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