Lab Manual: A Cone from a Sector of a Circle | Lab Manuals for Class 9 PDF Download

Objective

Materials Required

• A piece of wooden hardboard
• Acrylic sheets
• White paper
• Adhesive tape
• Scissors
• Geometry box
• Marker

Prerequisite Knowledge

• Concept of a circle.
• Concept of sector of a circle.
• Concept of a cone.

Theory

• For concept of a circle refer to Activity 23.
• Sector of the Circle:
  The region between an arc and the two radii joining the centre to the end points of the arc is called a sector.
  Sectors are of two types – minor sector and major sector. Minor sector is the sector of circle, which is less than a semi-circle and major sector is the sector of circle, which is greater than a semi-circle.
  Area of sector = (Arc length/Circumference of circle) x Area of circle
  
• Cone: A right circular cone is a solid generated by revolving a line segment which passes through a fixed point and which makes a constant angle with a fixed line.
  In other words, if a right angled triangle is revolved about one of the two sides forming a right angle, keeping the other sides fixed in position, then the solid so obtained by revolving the line segments is called a right circular cone.In, a right angled ∆OPA on revolving about the segment OP, generates a right circular cone in which ABC is a circle.

Procedure

• Take a piece of wooden hardboard of suitable size and by using adhesive, paste a white paper on it.
• From acrylic sheet, cut out a circle of radius l.
  
• Now, cut out a sector having angle θ° from the circle.
  
• To form a cone, bring together both the radii of the sector and by using a adhesive tape, attach the ends and fix it on the hardboard.
  

Demonstration

• Radius of the base of cone = r
• Slant height of the cone = Radius of circle = l
• Circumference of the base of cone = Arc length of sector = 2πr
• Now, curved surface area of cone = Area of the sector
  = Area of sector = (Arc length/Circumference of circle) x Area of the circle
  = (2πr/2πl) x πl²
  = πrl

Observation
By actual measurement,
The slant height (l) of the cone = ………… and radius (r) = …………
∴ Arc length, (l) = ………….
Area of the sector = ………….
curved surface area of the cone = …………
Hence, curved surface area of the cone = Area of the sector

Result
We have derived the formula for calculating the curved surface area of cone.

Applications
This result is useful in

• estimation of canvas required to make a conical tent.
  
• estimation of material required to make joker’s cap, ice-cream cone, etc.