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Sec 2   Term 3 Arc Length 01  97
Sec 2   Term 3 Arc Length 01  97
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Sec 2 Term 3 Arc Length 01 97

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  • 1. Name: ( ) Class : Date: Term 4 – e-Learning Lesson : Arc Length, Area of Sector and Segment 1. In the diagram, O is the centre of the circle and the radius of the circle is 4 cm. Find the length of the major arc APB. (Take π = 3.142, corrected to 3 decimal places.) 2. The diagram below shows the cross-section of a component for an engine in a pumping station. The circular arc BCD has centre A, radius 14 m and ∠ BAD = 60°. The semi-circle DEA has centre O and diameter 14 m. Taking π = 3.142, calculate (a) the length of the arc BCD, (b) the total perimeter of the cross-section ABCDEA. 3. A piece of wire is bent into a sector of a circle OPRQ such that the length of the major arc PRQ is 4.5 times the radius. Find the angle, x, subtended by the major arc at the centre of the circle. (Take π = 3.142, corrected to 3 decimal places.) 4. An arc PQ of a circle subtends an angle of 140° at the centre O. If the length of the minor arc PQ is 22 cm, calculate (i) the radius of the circle, (ii) the area of the minor sector OPQ. (Take π = 3.142, corrected to 3 decimal places.)) Page 1
  • 2. 5. The diagram shows two circles, centre P and Q, of radius 8 cm and 2 cm respectively, touching at point A. A common tangent touches the circles at B and at C. (i) Find, in degrees, the angle APB. For the shaded region ABC, find, correct to one decimal place, (ii) the perimeter, (iii) the area. (Take π = 3.142, corrected to 3 decimal places.) 6. In the diagram, PQRS is a sector of a circle with radius 5 cm and ∠ QPS = 36°. Find the area of the segment QRS. (Take π = 3.142, corrected to 3 decimal places.) 7. The diagram shows a cross section of a cylindrical drain of radius 2 m. Water is filled to a height of 1 m. Find the area and perimeter of the shaded region. (Take π = 3.142, corrected to 3 decimal places.) Page 2

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