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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.))
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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.)
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