Perimeter of Sectors and Segments

Continuous lines form the boundary of a closed geometric figure. In geometry, perimeter can be defined as a path or boundary around a shape. It can also be defined as the length of the contour of the shape.

The word perimeter comes from the Greek “peri”, which means around, and “metron”, which means measurement. Perimeter is the total length of the sides of a two-dimensional shape.

We often find the perimeter when placing Christmas lights or fenced backyard gardens around the house. Other examples may include finding the total length of the football field boundary or the length of the crochet or ribbon required to cover the border of the table mat.

  1. Perimeters of sectors and segments

2r + θ/360 x 2πr Perimeter of sector


  1. Area of sectors of a circle

θ/360 πr2


  1. Areas of segments of a circle

Area =  θ/360 x πr21/2r2 sin θ

Perimeter = 2r {sin θ/2 + θ/360}


  1. Relation between the sector of circle and the surface of a cone
  2. Surface Area and volume of shape

i. Cube

ii. Cuboid

iii. Cylinder

iv. Pyramids

v. Cone

vi. Prism


a. Cube

  1. Surface area (S) = 6 x 2

Length of diagonal = x √3

Volume of cube = Base x area x height

V = x3


b. Cuboid

i. Volume = Base x area x height


c. Cylinder

i. Curve surface area

2 x π x radius x height = 2πr


d. Total surface area

i. When both tops area closed

πr2 + πr2 + 2πrh (Area of base + area of top + curve surface area)

:. 2πr (r + h)


ii. When the top is opened

Area of base + curved surface area

= πr2 + 2πrh

= πr (r + 2h)


e. Volume = Base Area x height

= π r2 x h

= 2πrh


f. Cone

i. Curved surface area = πr1

ii. Total surface area

= Area of circular base + curved surface area

= πr2 + πr1 => πr (r + 1)

iii. Volume = 1/3 2πrh

iv. Slant edge 12 = r2 + h2

1 = √12 = √r2 + h2


g. Pyranoid

i. Surface Area => Base area + Area of the triangular faces

ii. Volume = 1/3 base area x height

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