Area of Part of a Circle

14 Grade 10 Essential Mathematics questions on Area of Part of a Circle, with worked marking schemes. 14 questions are available on this topic in full.

1. Question 1

   1 mark

   A flower bed at the entrance of a health centre is a semicircle of diameter 28 m. Taking $\pi =\frac{22}{7}$, what is the area of the flower bed?

   A. 308 m²

   B. 44 m²

   C. 1 232 m²

   D. 616 m²

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

2. Question 2

   6 marks

   In a circle of radius 10 cm, a chord cuts off a minor segment and the two radii drawn to the ends of the chord make an angle of 90° at the centre. Taking π = 3.142, (a) calculate the area of the minor sector, (b) calculate the area of the triangle formed by the two radii and the chord, (c) hence calculate the area of the minor segment, and (d) state which of the two segments of this circle is the larger.

   (6 marks)

   Marking scheme

   (a) Area of sector = $\frac{90}{360}\times 3.142\times 10^2$ (1); = 78.55 cm² (1). (b) Triangle is right-angled at the centre, area = $\frac{1}{2}$ × $10\times 10$ (1); = 50 cm² (1). (c) Minor segment = 78.55 − 50 = 28.55 cm² (1). (d) The major segment is larger (1).

3. Question 3

   4 marks

   A goat is tied with a rope 5 m long to a post fixed at a corner of a rectangular fenced field, so that it grazes over a quarter of a circle.

   (a) Taking π = 3.142, calculate the area of the ground the goat can graze.

   (b) State what happens to the grazed area if the rope is replaced with one twice as long.

   (4 marks)

   Marking scheme

   (a) Grazed area = $\frac{1}{4}$ × $\pi \times r^2$ identified (1); $\frac{1}{4}$ × $3.142\times 5^2$ = $\frac{1}{4}$ × 78.55 (1); = 19.64 m² (accept 19.6 m²) (1). (b) The grazed area becomes four times as large, because the area depends on the square of the rope length (1).

4. Question 4

   5 marks

   A semicircular window pane in a school library has a diameter of 1.4 m.

   (a) Taking $\pi =\frac{22}{7}$, calculate the area of glass needed for the pane.

   (b) Glass costs KSh 1 500 per square metre. Calculate the cost of the glass for one such pane.

   (5 marks)

   Marking scheme for this question

   Create a free account to see it

5. Question 5

   3 marks

   A sector of a circle of radius 21 cm has an angle of 120° at the centre. Taking $\pi =\frac{22}{7}$, calculate the area of the sector.

   (3 marks)

   Marking scheme for this question

   Create a free account to see it

6. Question 6

   1 mark

   A sector of a circle of radius 21 cm has an area of 231 cm². Taking $\pi =\frac{22}{7}$, what is the angle of the sector at the centre?

   A. 60°

   B. 90°

   C. 30°

   D. 120°

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

7. Question 7

   1 mark

   A rectangular sheet of roofing off-cut measures 10 cm by 6 cm. A semicircle whose diameter is equal to the 6 cm width is cut off from one of the shorter ends. Taking $\pi =\frac{22}{7}$, what is the area of the sheet that remains?

   A. 28.29 cm²

   B. 45.86 cm²

   C. 31.71 cm²

   D. 74.14 cm²

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

8. Question 8

   2 marks

   Distinguish between a sector and a segment of a circle.

   (2 marks)

   Marking scheme for this question

   Create a free account to see it

9. Question 9

   1 mark

   A sector whose angle at the centre is 90° has an area of 38.5 cm². Taking $\pi =\frac{22}{7}$, what is the radius of the circle from which the sector was cut?

   A. 14 cm

   B. 49 cm

   C. 7 cm

   D. 3.5 cm

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

10. Question 10

    4 marks

    The minute hand of a clock on the wall of a school hall is 14 cm long. Taking $\pi =\frac{22}{7}$, calculate the area swept out by the hand in 25 minutes.

    (4 marks)

    Marking scheme

    Fraction of a full turn = $\frac{25}{60}=\frac{5}{12}$ (1); area of full circle = $\frac{22}{7}\times 14\times 14=616$ cm² (1); area swept = $\frac{5}{12}\times 616$ (1); = 256.67 cm² (accept 256.7 cm² or 256 $\frac{2}{3}$ cm²) (1).

11. Question 11

    1 mark

    A sector of angle 150° is cut out of a circular metal disc of radius 6 cm and thrown away. Taking $\pi =\frac{22}{7}$, what is the area of the piece of disc that remains?

    A. 47.14 cm²

    B. 33.0 cm²

    C. 113.14 cm²

    D. 66.0 cm²

    (1 mark)

    Marking scheme for this question

    Create a free account to see it

12. Question 12

    5 marks

    A circular fish pond of radius 7 m is surrounded by a concrete path of uniform width 3.5 m. Taking $\pi =\frac{22}{7}$, calculate the area of the concrete path.

    (5 marks)

    Marking scheme

    Outer radius = 7 + 3.5 = 10.5 m (1); area of outer circle = $\frac{22}{7}\times 10.5\times 10.5=346.5m^2$ (1); area of pond = $\frac{22}{7}\times 7\times 7=154m^2$ (1); path area = outer area − pond area (1); = $346.5-154=192.5m^2$ (1).

13. Question 13

    1 mark

    A round chapati of radius 14 cm is cut through the centre into 8 equal sectors. Taking $\pi =\frac{22}{7}$, what is the area of the top surface of one piece?

    A. 616 cm²

    B. 77 cm²

    C. 38.5 cm²

    D. 154 cm²

    (1 mark)

    Marking scheme for this question

    Create a free account to see it

14. Question 14

    1 mark

    A sector of a circular lawn has a radius of 12 m and an angle of 150° at the centre. Taking π = 3.142, what is the area of the sector?

    A. 188.52 m²

    B. 31.42 m²

    C. 226.22 m²

    D. 452.45 m²

    (1 mark)

    Marking scheme for this question

    Create a free account to see it

15. 10 more marking schemes are on this page. A free account opens all of them, and lets you build your own paper on the topics you have actually taught, laid out in KNEC format with its full marking scheme.

    Create a free account

More Grade 10 Essential Mathematics topics