Lab Manual: Comparison of Volumes of Two Right Circular Cylinders | Lab Manuals for Class 10 PDF Download

Objective

Prerequisite Knowledge
To make a cylinder from a rectangular sheet.
Circumference of circle = 2πr and area of circle = πr² where r is the radius of the circle.
Volume of right circular cylinder =πr²h (r→ radius of circular base and h is the height of the cylinder)

Materials Required
Coloured glaze paper, a pair of scissors, cellotape, geometry box, fevicol.

Procedure

• Cut two rectangles of same dimensions as l = 22 cm and b = 10 cm.
• Name them as rectangle 1 and rectangle 2.
  
• Curve the rectangle 1 along its length and join the ends with cellotape to get a cylinder.
  
• Curve the rectangle 2 along its breadth and join the ends with cellotape to get another cylinder.
  

Observation
For rectangle 1:
length of the rectangle = circumference of the circular base of the cylinder
i.e. l = 2πr₁ = 22 cm.
r₁ = 11/x
breadth of the rectangle = height of the cylinder
i.e. b = h1 = 10 cm.
V₁= πr²h₁ =

For rectangle 2:
breadth of the rectangle = circumference of circular base of the cylinder
b = 2πr₂ = 10 cm
r₂ = 10/2π = 1.59 cm
length of the rectangle = height of the cylinder
l = h₂ = 22 cm.
V₂ = πr²h₂   

Result
Volume of these two cylinders are not same.

Learning Outcome
Students can easily understand the concept that the volume of the right circular cylinder formed by curving a rectangular sheet along its length not equal to the volume of the cylinder formed by curving another rectangular sheet of same dimensions along its breadth.

Activity Time
A cylinder is formed by curving a rectangular sheet 22 cm x 20 cm along its length. Another cylinder is formed by curving a squared sheet of side 22 cm along its any side. Compare the volume of two cylinders so formed.