Lab Manual: Curved Surface Areas & Total Surface Areas of Two Right Circular Cylinder | Lab Manuals for Class 10 PDF Download

Objective

• Construction of a cylinder from rectangular sheet by paper folding.
• Area of rectangle = length X breadth
• Circumference and area of a circle.
  C=2πr , A = πr²

Materials Required
Coloured glazed paper, sketch pens, a pair of scissors, fevicol, cellotape, geometry box.

Procedure

• Take two rectangular sheets of paper of same dimensions as l= 14 cm and b =7 cm named as rectangle 1 and rectangle 2.
  
• Curve the rectangle 1 along its length l=14 cm.
• Join two ends with cellotape to get a cylinder.

• Similarly curve the rectangle 2 along its breadth b = 7 cm to get another cylinder as shown in figure.
  

Observation
For rectangle 1:
length of the rectangle = circumference of the circular base of the cylinder
l = 2πr₁ = 14 cm.
r₁ = 14/2π = 7/π
breadth of the rectangle = height of the cylinder
b = h = 7 cm
curved surface area C₁ = 2πr₂h₂ = 6π x 7/2π x 14 = 98cm²
Total surface area T₁ = 2πr₁² + C₁ = 2π x 49/π² = 98(1 + π/ π)

For rectangle 2:
breadth of the rectangle = circumference of circular base of the cylinder
b=2πr₂ = 7 cm
r₂ = 7/2π
length of the rectangle = height of the cylinder
l= h₂ = 14 cm.
curved surface area C₂ = 2πr₂h_{2 = 2π x 7/2π x 14 = 98 cm}²
Total surface area T₂ = 2πr₂² + C₂
=

Result

• The curved surface areas (or lateral surface areas) of two cylinders of different height and radius formed from the two rectangular sheets of paper of same dimensions are same.
• The total surface areas of two cylinders of different height and radius formed from the two rectangular sheets of paper of same dimensions are not same.

Learning Outcome
Concept of comparison of curved surface area and total surface area of two cylinders formed from the two rectangular sheets of paper of same dimension is more clear. Students can understand easily that

Activity Time
Take a rectangular sheet of paper of size 22 cm x 10 cm. Form two cylinders
(i) curved along its length
(ii) curved along its breadth.
Compare the lateral surface areas and total surface areas of these two cylinders.