1. 10.4 Length of an Arc and Area of a Sector
Additional Example 7
Additional Example 8
Additional Example 9
Additional Example 10
© SNP Panpac (H.K.) Ltd.

2. Additional Example 7
In the figure, AOB is a sector of a circle with centre O. The area of the sector is 60 cm2 and AOB = 45.
Solution
(a) Find the radius of the sector.
(Give the answers correct to 2 decimal places.)
(b) What is the length of ?
Solution
© SNP Panpac (H.K.) Ltd.

3. Solution (a) Let r cm be the radius of the sector. Area of a sector
Additional Example 7
In the figure, AOB is a sector of a circle with centre O. The area of the sector is 60 cm2 and AOB = 45.
(a) Find the radius of the sector.
(b) What is the length of ?
(Give the answers correct to 2 decimal places.)
Solution
Area of a sector
(a) Let r cm be the radius of the sector.
r =
Q7(b)
= 12.36
 The radius of the sector is cm.
© SNP Panpac (H.K.) Ltd.

4. Solution (b) The length of Arc length From (a), r = 12.360 8 = 9.71 cm
Additional Example 7
In the figure, AOB is a sector of a circle with centre O. The area of the sector is 60 cm2 and AOB = 45.
(a) Find the radius of the sector.
(b) What is the length of ?
(Give the answers correct to 2 decimal places.)
Solution
(b) The length of
Arc length
From (a), r =
= 9.71 cm
© SNP Panpac (H.K.) Ltd.

5. Additional Example 8
In the figure, OAC is a semicircle with centre O and radius 42 cm is an arc with centre D and radius BD. Find the perimeter of the figure.
(Take  = )
Solution
© SNP Panpac (H.K.) Ltd.

6. Solution Arc length = 132 cm AC = 2  OA = 2  42 cm = 84 cm BD = AC
Additional Example 8
In the figure, OAC is a semicircle with centre O and radius 42 cm is an arc with centre D and radius BD. Find the perimeter of the figure.
Solution
(Take  = )
Arc length
= 132 cm
AC = 2  OA
= 2  42 cm
= 84 cm
BD = AC
= 84 cm
( ABDC is a rectangle.)
CD = BD
= 84 cm
(radius of circle)
 AB = CD
= 84 cm
© SNP Panpac (H.K.) Ltd.

7. Solution Arc length = 132 cm Perimeter = + AB + = (132 + 84 + 132) cm
Additional Example 8
In the figure, OAC is a semicircle with centre O and radius 42 cm is an arc with centre D and radius BD. Find the perimeter of the figure.
Solution
(Take  = )
Arc length
= 132 cm
Perimeter = AB +
= ( ) cm
= 348 cm
© SNP Panpac (H.K.) Ltd.

8. Additional Example 9
Given that the area of a sector is 80 cm2 and the angle of the sector is 80, find the radius of the sector. (Give the answer correct to 2 decimal places.)
Solution
© SNP Panpac (H.K.) Ltd.

9. Solution Let r cm be the radius of the sector. Area of a sector
Additional Example 9
Given that the area of a sector is 80 cm2 and the angle of the sector is 80, find the radius of the sector. (Give the answer correct to 2 decimal places.)
Solution
Let r cm be the radius of the sector.
Area of a sector
r = 10.70
 The radius of the sector is cm.
© SNP Panpac (H.K.) Ltd.

10. Additional Example 10
In the figure, the radius of sector AOB is 4 cm and AOB = 90. Find
(Give the answers correct to 2 decimal places.)
(a) the perimeter of the shaded region,
Solution
Solution
(b) the area of the shaded region.
© SNP Panpac (H.K.) Ltd.

11. Solution (a) In AOB, (Pyth. Theorem) AB2 = AO2 + OB2
Additional Example 10
In the figure, the radius of sector AOB is 4 cm and AOB = 90. Find
(a) the perimeter of the shaded region,
(b) the area of the shaded region.
(Give the answers correct to 2 decimal places.)
Solution
(a) In AOB,
(Pyth. Theorem)
AB2 = AO2 + OB2
© SNP Panpac (H.K.) Ltd.

12. Solution Arc length = 2 cm Perimeter = AB + = 11.94 cm Q10(b)
Additional Example 10
In the figure, the radius of sector AOB is 4 cm and AOB = 90. Find
(a) the perimeter of the shaded region,
(b) the area of the shaded region.
(Give the answers correct to 2 decimal places.)
Solution
Arc length
= 2 cm
Perimeter = AB +
Q10(b)
= cm
© SNP Panpac (H.K.) Ltd.

13. = Area of sector AOB – Area of AOB
Additional Example 10
In the figure, the radius of sector AOB is 4 cm and AOB = 90. Find
(a) the perimeter of the shaded region,
(b) the area of the shaded region.
(Give the answers correct to 2 decimal places.)
Solution
(b) Area
= Area of sector AOB – Area of AOB
= 4.57 cm2
Area of a sector
© SNP Panpac (H.K.) Ltd.