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# Form 2 Mathematics Questions and Answers on Area of Part of a Circle

Form 2 Mathematics Questions and Answers on Area of Part of a Circle.

All answers are in video format.

Lessons (**16**)

- 1.
The figure below shows two intersecting circles of radius 9 cm each with centre #0_1# and #0_2#.
Find:
(a) the length of the common chord AB.
(b) the area of the shaded region. (Take #pi#=3.142)

7m 7s - 2.
The figure below shows two intersecting circles with centres #O_1# and #O_2# having radii 4 cm and 3 cm respectively. #angleAO_1B# = 57.64° and #angleAO_2B# = 80°. #O_1 O_2# is a perpendicular bisector of AB. (Take #pi#=3.142)
Calculate:
(a) the length of AB.
(b) the area of the shaded region.

6m 50s - 3.
Find the area of the shaded region in the figure below, given that the two circles with centres #O_1# and #O_2# have radii 10 cm and 8 cm respectively. #angleAO_1B# = 90° and #angleAO_2B# = 124.2°. (Take #pi#=3.142)

3m 14s - 4.
Find the common area between the two intersecting circles in the figure below. The circle centres #O_1# and #O_2# have radii 18 cm and 12 cm respectively and the chord AB is 18 cm long. (Take #pi#=3.142)

4m 33s - 5.
(Take #pi# =22/7)
A sector of a circle of radius r has angle ? subtended at the centre. Calculate the area of the sector if:
(a) r = 1.4 cm, #theta# = 30°
(b) r = 2.1 cm, #theta# = 45°
(c) r = 8 cm, #theta# =33°
(d) r = 8.4 cm, #theta# = 60°

3m 54s - 6.
(Take #pi# =22/7)
A sector of a circle of radius r has angle ? subtended at the centre. Calculate the area of the sector if:
(a) r = 9.1 cm, #theta# =24°
(b) r = 4 cm, #theta# = 259°
(c) r = 10 cm, #theta# = 301°

2m 24s - 7.
A flood light can spread its illumination over an angle of 50° to a distance of 49 cm. Calculate the area that is lit by the flood light. (Take #pi# =22/7)

1m 22s - 8.
The shaded region in the figure below shows the area swept out on a flat windscreen by a wiper. Calculate the area of this region. (Take #pi# =22/7)

3m 4s - 9.
The two arms of a pair of dividers are spread so that the angle between them is 45°. Find the area of the sector formed if the length of an arm is 8.4 cm. (Take #pi# =22/7)

1m 44s - 10.
A goat is tethered at the corner of a fenced rectangular grazing field. If the length of the rope is 21 m, what is its grazing area? (Take #pi# =22/7)

2m 22s - 11.
A chord XY of length 12 cm is drawn in a circle with centre 0 and radius 10 cm, as in the figure below. (Take #pi#=3.142)
Calculate:
(a) the distance ON.
(b) the area of the sector OXPY.
(c) the area of triangle OXY.
(d) the area of the minor segment.
(e) the area of the major segment.

5m 35s - 12.
A chord XY subtends an angle of 120° at the centre of a circle of radius 13 cm. Calculate the area of the minor segment. (Take #pi#=3.142)

2m 55s - 13.
The figure below shows a circle with centre 0 and radius 4#root#2 cm. If the length of the chord AB is 8 cm, show that the shaded area is #(8pi - 16) cm^2#.

4m 27s - 14.
The figure below, ADC is a chord of a circle with centre 0 passing through A, B and C. BD is a perpendicular bisector of AC. AD = 3 cm and BD = 1 cm. (Take #pi#=3.142)
Calculate:
(a) the radius OA of the circle.
(b) the area of the sector OABC.
(c) the area of the segment ABCD.

5m 31s - 15.
The figure below shows an arc ACE of a circle of radius 6 cm. If BC = CD = 4 cm, calculate the area of the shaded region. (Take #pi#=3.142)

6m 32s - 16.
In the figure below, ABC is an arc of a circle with centre 0 and radius 7 cm. The arc subtends an angle of 60° at the centre and AE = DC = AC = ED = 7 cm. Calculate the area of the figure ABCDE. (Take #pi#=3.142)

3m 16s