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Contents
Area of Sector & Length of Arc
Surface Area of Cones & Pyramids
|
Length
of Arc & Area of Sector Consider the sector OAQB in the figure on the right. BOA is 40°. The length of arc AB which subtends this angle is 40 of 360 equal parts of the circumference. Thus, length of arc APB = 40/360 x circumference Also the area of sector OAQB = 37/360 x area of circle. In general, we have: Length of arc = q
2pr
360
Area
of sector = q
pr2
360
Example
(i) the sector QOR,
(ii) the sector
POQ.
(b)
If the circumference of the circle is 64cm, calculate the length of
(i)
arc PQ,
(ii)
major arc RSP
Area
sector QOR = 100/360 x 48cm2
= 13.3 cm2 (3 s.f.)
Area
sector POQ = 40/360 x 48cm2
= 5.33 cm2 (3 s.f.)
Arc
PQ = 40/360 x 64cm
= 7.14 cm (3 s.f.)
Arc
RSP = 240/360 x 64cm
= 42.7 cm (3 s.f.)
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(a) In the figure on the right, if the area of the circle is given to be 48cm2, calculate the area of
