Lab Manual: Surface Area of a Cone | Lab Manuals for Class 10 PDF Download

Objective

Prerequisite Knowledge
Area of circle = πr²
Area of parallelogram = b x h (b = base, h = height).
Circumference of circle = 2πr

Materials Required
A cone made of chart paper, a pair of scissors, geometry box, fevicol, cello tape.

Procedure

• Make a cone of pink chart paper having base radius r, slant height ‘l’ and height h.
• Cut the cone along slant height as shown in fig (i) as per dotted line and unroll it to get a sector, as shown in fig. (ii). Name this sector OAB.
• Identify the arc length AB of the sector OAB = circumference of the base of the cone. radius of the sector OAB = slant height of the cone. As shown in the fig. (ii).
• Cut the sector OAB into 4 small equal sectors, along dotted lines as shown in fig. (ii) and fill red colour in two sectors as shown.
• Arrange these small sectors to get a parallelogram as shown in fig. (iii).
  

Observation

• Base of parallelogram
  
• Altitude of parallelogram = slant height of cone = l
• Area of parallelogram =2πr x l = Curved surface area of cone.
• Total surface area of cone = 2πrl + area of circular base of cone.
  = 2πrl +  πr²
  = πr(l+r)

Learning Outcome
Students will learn the concept to differentiate between the curved surface area and total surface area of a cone.

Activity Time

•  Find lateral surface area of a cone in figure given.
•  Find total surface area of a cone in figure given.