10.4 Length of an Arc and Area of a Sector

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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.

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.

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 = 12.360 8 Q7(b) = 12.36  The radius of the sector is 12.36 cm. © SNP Panpac (H.K.) Ltd.

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 = 12.360 8 = 9.71 cm © SNP Panpac (H.K.) Ltd.

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.

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.

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 + = (132 + 84 + 132) cm = 348 cm © SNP Panpac (H.K.) Ltd.

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.

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 10.70 cm. © SNP Panpac (H.K.) Ltd.

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.

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.

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) = 11.94 cm © SNP Panpac (H.K.) Ltd.

= 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.