GCSE - Numeracy and Mathematics
Tier: Higher
Grade: A/A*
Topic: Length of arc, Perimeter and area of
sectors and segments
Starter
Top Tips!
Calculate the perimeter of the sector:
Key parts of a circle:
a)
b)
13 cm
17.3cm
Examination Question: 2012 Summer Link Applications U2 Higher Q13
Skills:
1. Calculate the length of the arc AB.
The diagram shows a circular flower bed, which is split into two
sectors, one for spring flowers and the other for roses.
The centre of the circle is O and the area of the minor sector is
31·3 𝑚2 .
2. Find the area of the sector AOB.
3. Calculate the area of the segment.
a) Calculate the radius of the flower bed.
[3]
b) Calculate the perimeter of the major sector of the flower bed.
[3]
Assessment for Learning
Video / QR code
GCSE - Numeracy and Mathematics
Tier: Higher
Grade: A/A*
Topic: Length of arc, Perimeter and area of
sectors and segments
Starter
Top Tips!
Calculate the perimeter of the sector:
Key parts of a circle:
a)
b)
13 cm
17.3cm
a) 32+32+17.3 = 81.3cm
b) 8+8+13 = 29 cm
Examination Question: : 2012 Summer Link Applications U2 Higher Q13
The diagram shows a circular flower bed, which is split into two
sectors, one for spring flowers and the other for roses.
Skills:
1. Calculate the length of the arc AB.
Length of arc
=
=
𝜃
360
45
360
× 𝜋 ×𝑑
The centre of the circle is O and the area of the minor sector is
31·3 𝑚2 .
× 𝜋 × 24
= 9.4 cm (1.d.p)
a) Calculate the radius of the flower bed.
2. Find the area of the sector AOB.
80
31.3 = 360 × 𝜋 × 𝑟 2
Area of sector
=
=
𝜃
360
45
360
× 𝜋𝑟 2
𝑟2 =
× 𝜋 × 102
= 39.3 𝑐𝑐2 (1.ll.d)
3. Calculate the area of the segment.
31.3
80
×𝜋
360
𝑟 = 6.7m (1.d.p)
[3]
b) Calculate the perimeter of the major sector of the flower bed.
74
A sector = 360 × 𝜋 × 82 = 41.3𝑚2
A triongl =
=
1
2
1
2
𝑎𝑎 sin 𝐶
× 8 × 8 × sin 74 = 30.8𝑚2
A segment = 41.3 – 30.8 = 10.5𝑚
Assessment for Learning
[3]
2
Video / QR code