Mensuration (II) 13.53
MC Question Tutor
Example 2
In the figure, OAB and OCD are sectors with centre O, where OA = 18 cm and
OC = 30 cm. The area of the shaded region ABDC is 192r cm2. Which of the
following is/are true?
I. The angle of the sector OAB is 120c.
II. The area of the sector OAB is 108r cm2.
III. The perimeter of the shaded region is 32r cm.
A. I only C. I and II only
B. III only D. II and III only
Solution
I. Let +AOB = xc.
Area of sector OCD - area of sector OAB = 192r cm2
x
360c
c # r # 302 - x
360c
c # r # 182 = 192r
2.5rx - 0.9rx = 192r
1.6rx = 192r
x = 120
` I is true.
II. Area of sector OAB = 360
012 c
c # r # 182 cm2 = 108r cm2
` II is true.
III. Perimeter of the shaded region
= AC + BD + AB
% + CD
%
= ()()
30 18 30 18 218230
360
120
360
120
## ##
rr
-+-+ +
c
c
c
c
:D
cm
= (24 + 32r) cm
` III is not true.
` The answer is C.
Exam Drill 2
In the figure, OPQ and ORS are sectors with centre O, where OP = 6 cm
and PR = 4 cm. The area of the shaded region PQSR is 8r cm2. Which of
the following is/are true?
I. The angle of the sector OPQ is 45c.
II. The perimeter of the sector OPQ is 2
3r cm.
III. The area of the sector ORS is 2
5r cm2.
A. I only C. I and III only
B. II only D. II and III only
O
A
B
D
C
Diagram Clue
O
30 cm
x°D
C - O
18 cm B
A
x°
◀
Diagram Clue
O
A
B D
C
◀
R S
Q
P
O
13.52 Chapter 13
Public Exam Questions
HKDSE 2017 (A2)
1. In the figure, OPQR is a quadrilateral such that OP = OQ = OR. OQ
and PR intersect at the point S. S is the mid-point of PR.
(a) Prove that 3OPS , 3ORS.
(b) It is given that O is the centre of the circle which passes
through P, Q and R. If OQ = 6 cm and +PRQ = 10c, find the
area of the sector OPQR in terms of r.
HKDSE 2015 (A1)
2. The radius and the area of a sector are 12 cm and 30r cm2 respectively.
(a) Find the angle of the sector.
(b) Express the perimeter of the sector in terms of r.
HKDSE 2013 (A2)
3. In a workshop, 2 identical solid metal right circular cylinders of base
radius R cm are melted and recast into 27 smaller identical solid
right circular cylinders of base radius r cm and height 10 cm. It is
given that the base area of a larger circular cylinder is 9 times that
of a smaller one.
(a) Find (i) r : R, (ii) the height of a larger circular cylinder.
HKDSE 2018 (A)
4. In the figure, O is the centre of the sector
OABCD. AD and OC are perpendicular to
each other and intersect at the point E.
F is a point lying on AD such that BF is
perpendicular to AD. If AF = 9 cm,
DF = 39 cm and OE = 18 cm, then the area
of the sector OBC is
A. 48r cm2.
B. 75r cm2.
C. 96r cm2.
D. 150r cm2.
HKDSE 2016 (A)
5. In the figure, OAB and OCD are sectors with
centre O, where OA = 33 cm and OC = 39 cm.
The area of the shaded region ABDC is 72r cm2
.
Which of the foll
I. The angle of
II. The area of
III. The perimeter
A. I only
B. II only
C. I and III only
D. II and III only
HKDSE 2012 (A)
6. In the figure, OA
centre O. If AB
! =
and OA = 30 cm,
A. 5 cm.
B. 10 cm.
C. 20 cm.
D. 40 cm.
O
C
B
F
E
O
A
D
13.52 Chapter 13
Public Exam Questions
HKDSE 2017 (A2)
1. In the figure, OPQR is a quadrilateral such that OP = OQ = OR. OQ
and PR intersect at the point S. S is the mid-point of PR.
(a) Prove that 3OPS , 3ORS.
(b) It is given that O is the centre of the circle which passes
through P, Q and R. If OQ = 6 cm and +PRQ = 10c, find the
area of the sector OPQR in terms of r.
HKDSE 2015 (A1)
2. The radius and the area of a sector are 12 cm and 30r cm2 respectively.
(a) Find the angle of the sector.
(b) Express the perimeter of the sector in terms of r.
HKDSE 2013 (A2)
3. In a workshop, 2 identical solid metal right circular cylinders of base
radius R cm are melted and recast into 27 smaller identical solid
right circular cylinders of base radius r cm and height 10 cm. It is
given that the base area of a larger circular cylinder is 9 times that
of a smaller one.
(a) Find (i) r : R, (ii) the height of a larger circular cylinder.
HKDSE 2018 (A)
4. In the figure, O is the centre of the sector
OABCD. AD and OC are perpendicular to
each other and intersect at the point E.
F is a point lying on AD such that BF is
perpendicular to AD. If AF = 9 cm,
DF = 39 cm and OE = 18 cm, then the area
of the sector OBC is
A. 48r cm2.
B. 75r cm2.
C. 96r cm2.
D. 150r cm2.
Which of the following is/are true?
I. The angle of the sector OAB is 60c.
II. The area of the sector OAB is 11r cm2.
III. The perimeter of the sector OCD is 13r cm.
A. I only
B. II only
C. I and III only
D. II and III only
HKDSE 2012 (A)
6. In the figure, OAB and OCD are sectors with
centre O. If AB
! = 12r cm, CD
% = 16r cm
and OA = 30 cm, then AC =
A. 5 cm.
P
Q
S
R
O
C
B
F
E
O
A
D
C
B
O
A
D
O
7
配合不同學生口味,照顧學習差異。
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Book 2B Ch.13•P.13.53-13.54
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