Chap10

AP

T ER

CH

10

Circles

1. By using the letters given in the diagram, complete the given table. Part of circle

D

(a)

C

Example(s)

Radius

(b) Diameter (c)

O

B

A

E

Chord

(d) Semicircle (e)

Minor arc

(f)

Major arc

(g) Minor sector (h) Major sector (i)

Segment

2. By using a pair of compasses and a ruler, draw the following parts of a circle. (a) A circle with centre P and a radius of 1.5 cm.

  

P



(b) (i) A circle with TU as its radius and T as the centre. (ii) A chord UR of 2 cm. U



T

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3. By construction, show the centre O of the circle below. Hence, measure the length of the radius.

22 4. Calculate the circumference of a circle with diameter 2.1 m. 1Use � = — 72 22 5. Calculate the circumference of a circle with radius 2.8 m. 1Use � = — 72 6. Find the diameter of circle with circumference 37.5 m. (Use � = 3.14) 7. Find the radius of a circle with circumference 63.5 mm. (Use � = 3.14) 8. Solve each of the following problems. (a) A round-shape cake has a circumference of 54 cm. What is the radius of the cake? (Use � = 3.142) (b)



A ball fits exactly into a square box as shown in the diagram. If the length of the box 22 is 21 cm, find the circumference of the circle. 1Use � = — 72

22 9. Calculate the arc length of the following sector. 1Use � = — 72

O

75° 4.2 cm

22 10. Find the angle subtended at the centre of the following sector. 1Use � = — 72 P Arc length = 29.33 cm

21 cm

θ O

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Q

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22 11. Calculate the radius of the following sector. 1Use � = — 72 28 cm P

Q 56° O

12. A 4 cm 37° 8 cm

E

D

B

6 cm

C

In the diagram, ABC is a right-angled triangle with AB = 8 cm and BC = 6 cm. ADE is a sector with centre A and ∠DAE = 37°. Find the perimeter of the shaded region. (Use � = 3.142) 13. Calculate the area of the circle below. (Use � = 3.14) O Diameter = 15 cm

14. Calculate the radius and the diameter of a circle with area 202.25 cm2. (Use � = 3.142) 15. Calculate the radius and the area of a circle with circumference 24.43 cm. (Use � = 3.142) 16. Calculate the radius and the circumference of a circle with area 3160 cm2. 22 1Use � = — 72

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17. A

C

B

The diagram shows two semicircles with diameter AB and BC respectively. Given that 5  � cm2, calculate the AB = 2r cm and BC = 3r cm. If the area of the shaded region is 40 — 8 value of r. 18. Calculate the area of the sector below. (Use � = 3.142) A

165°

O 4.5 cm

B

19. Calculate the angle subtended at the centre of a sector with area 13.86 m2 and radius 5.4 m. (Use � = 3.14) 20. Calculate the radius of a sector with area 1.9625 cm2 and angle subtended at the centre is 36°. (Use � = 3.14) 21. 2r cm

A

O

r cm

B

C

The diagram above shows a trapezium OABC and a quadrant OAC. Given that OC = r cm and AB = 2r cm and the area of the shaded region is 5.6 cm2, calculate the value of r. 22 1Use � = — 72

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