Mathematics 10 Quarter 3

1. SEGMENTS AND
SECTORS OF A
CIRCLE & ARC
LENGTH
MATHEMATICS 10
QUARTER 2
BY TEACHER ESTELA JOY A. SOL
objective
s
review
sector
segmen
t
arc
length
exercis
e

2. objective
review
sector
segmen
t
arc
length
exercis
e After going through this topic,
you are expected to:
• illustrate segments and
sectors of a circle,
• identify segments and
sectors given an illustration,
• solve problems involving
arc length, segments and
sectors of a circle.

3. objective
review
sector
segmen
t
arc
length
exercis
e PARTS OF A CIRCLE

4. objectiv
review
sector
segmen
t
arc
length
exercis
e A is
the region bounded by
an arc of the circle and
the two radii to the
endpoints of the arc.
𝐴 =
𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑟𝑐
360
(𝜋𝑟2
)
To find the area of a sector of a circle,
P
A
L

5. objectiv
review
sector
segmen
t
arc
length
exercis
e
𝐴 =
𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑟𝑐
360
(𝜋𝑟2
)
𝐴 = 𝜋𝑟2
𝐴 =
1
2
𝜋𝑟2
𝐴 =
1
4
𝜋𝑟2

6. objectiv
review
sector
sector
A
B
C
segmen
t
arc
length
exercis
e Example 1
𝐴 =
𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑟𝑐
360
(𝜋𝑟2
)
The radius of ⨀𝐶 is 10𝑐𝑚 . If
𝑚∠𝐴𝐶𝐵 = 60 , what is the area of
sector 𝐴𝐶𝐵?
𝐴 =
60
360
(3.14)(102
) =
1
6
(3.14)(100)
=
1
6
(314) = 52.33𝑐𝑚2
60°

7. objective
review
sector
segmen
t
arc
length
exercis
e A is
the region bounded by an
arc and the segment
joining its endpoints.
𝐴 = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑒𝑐𝑡𝑜𝑟 − 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒
𝐴𝑠𝑒𝑔𝑚𝑒𝑛𝑡 =
𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑟𝑐
360
(𝜋𝑟2
) −
𝑏ℎ
2
To find the area of the segment
of a circle,
E
F
D

8. objective
review
sector
segmen
t
arc
length
exercis
e Example
2
𝐴 = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑒𝑐𝑡𝑜𝑟 − 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒
𝐴𝑠𝑒𝑔𝑚𝑒𝑛𝑡 =
𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑟𝑐
360
(𝜋𝑟2
) −
𝑏ℎ
2
Find the area of the segment
bounded by 𝐸𝐹 of ⨀𝑂 on the
right.
5 𝑖𝑛
𝑆𝑡𝑒𝑝 1 𝑆𝑡𝑒𝑝 2
𝑆𝑡𝑒𝑝 3 – 𝑆𝑢𝑏𝑡𝑟𝑎𝑐𝑡 𝑡ℎ𝑒 𝑟𝑒𝑠𝑢𝑙𝑡𝑠
O
E
F

9. objective
review
sector
segmen
t
arc
length
exercis
e Example
2
𝐴𝑠𝑒𝑐𝑡𝑜𝑟 =
𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑟𝑐
360
(𝜋𝑟2
)
Find the area of the segment
bounded by 𝐸𝐹 of ⨀𝑂 on the
right.
𝑺𝒕𝒆𝒑 𝟏 − 𝑭𝒊𝒏𝒅 𝒕𝒉𝒆 𝒂𝒓𝒆𝒂 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒄𝒕𝒐𝒓.
=
90
360
(𝜋𝑟2
) =
1
4
(3.14)(52
)=
1
4
(3.14)(25)
=
1
4
(78.5) = 19.63𝑖𝑛2
5 𝑖𝑛
O
E
F

10. objective
review
sector
segmen
t
arc
length
exercis
e Example
2
𝐴∆ =
𝑏ℎ
2
Find the area of the segment
bounded by 𝐸𝐹 of ⨀𝑂 on the
right.
𝑺𝒕𝒆𝒑 𝟐 − 𝑭𝒊𝒏𝒅 𝒕𝒉𝒆 𝒂𝒓𝒆𝒂 𝒐𝒇 𝒕𝒉𝒆 𝒕𝒓𝒊𝒂𝒏𝒈𝒍𝒆.
=
(5)(5)
2
=
25
2
= 12.5 𝑖𝑛2
𝑺𝒕𝒆𝒑 𝟑 − 𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕.
𝐴𝑠𝑒𝑔𝑚𝑒𝑛𝑡 = 19.63 − 12.5 = 7.13𝑖𝑛2
Therefore, the area of the segment
bounded by 𝑬𝑭 of ⨀𝑶 is 𝟕. 𝟏𝟑𝒊𝒏𝟐
5 𝑖𝑛
O
E
F

11. objective
review
sector
segmen
t
arc
length
exercis
e
refers to the
distance between two
points along a curve's
section.
To solve for the length of an arc,
𝓁 =
𝑎𝑟𝑐
360
(2𝜋𝑟)
where 𝑎𝑟𝑐 – is the degree
measure of the arc
M
N

12. objective
review
sector
segmen
t
arc
length
exercis
eAn arc of a circle
measures 45°. If the
radius of the circle is 6
cm, what is the length of
the arc?
𝓁 =
𝑎𝑟𝑐
360
2𝜋𝑟
Example
3 45°
6cm
=
45
360
2)(3.14)(6
=
1
8
37.68 = 4.71𝑐𝑚
M
N

13. objectives
review
sector
segmen
t
arc
length
exercis
e
A circular mat has a diameter of 53
cm. Lily wants to sew a 60°decorative
cloth on the mat . How many
centimeters squared of cloth does she
need? Give your answer to the nearest
tenth of a centimeter.
Given: 𝑟 = 26.5𝑐𝑚 𝑎𝑟𝑐 = 60°
𝐴𝑠𝑒𝑐𝑡𝑜𝑟 =
𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑟𝑐
360
(𝜋𝑟2
)
=
60
360
(3.14)(26.52
) =
1
6
(3.14)(702.25)
=
1
6
(2,205.065)= 367.51𝑐𝑚2
Solution:

14. Let’s Try!!
SelahandShalomatetogethera12“pizza.The
pizzawascutinto12equalpartslikethepictureon
heright. Theyhavealeftoverof4slices andgaveit
toastreetchild.Howmuchinchessquaredofthe
pizzadoesthestreet childhave?
Given: 𝒓 = 12÷2 =
𝟔" ;
Solution:𝐴 =
𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑜𝑓𝑡ℎ𝑒𝑎𝑟𝑐
360
(𝜋𝑟2) =
120
360
(3.14)(62
)
× 4 = 𝟏𝟐𝟎°
=
1
3
(3.14)(36) =
1
3
113.04 = 37.68𝑖𝑛2
𝒂𝒓𝒄 = 360÷12 = 30°

15. SEGMENTS AND
SECTORS OF A
CIRCLE & ARC
LENGTH
MATHEMATICS 10
QUARTER 2
BY TEACHER ESTELA JOY A. SOL
objective
s
review
sector
segmen
t
arc
length
exercis
e
Good job everyone!
God Bless!