Surface area of a cylinder

As performed in real lab:

Materials Required

Cylinder of known dimension, pair of scissors, gum, ruler.

Procedure:

  • Remove the top and bottom circles of the cylinder. [Fig(a)]
  • Make a vertical cut in the curved surface and lay the cylinder flat. [Fig(b)]
  • Measure the length and breadth of the rectangle so formed.

        

                Fig(a)                                                      Fig(b)

As performed in simulator:

  • Create a right circular cylinder by providing radius for the base and height for the curved surface.
  • Click on button "Draw Cylinder" to draw cylinder.
  • Click on top & bottom to separate out the bases from top and bottom of the cylinder.
  • Click on the cylinder to cut it and unroll to form a rectangle.

Observations:

  • The base and top of the cylinder are congruent circular regions.
  • The curved surface area of the cylinder opens to form a rectangular region.
  • The breadth of the rectangle is the height of the cylinder.
  • The length of the rectangle is the circumference of the base of the cylinder.
  • Curved surface area of cylinder(c)=area of rectangle

                                                         c= l x b

                                                 Since l= 2.π.r

                                                         b= h

                                                         c= l x b= 2.π.r.h

  • Total surface area of cylinder = curved surface area (c) + 2 (area of base circle)

                                                         = 2.π.r.h + 2.π.r²

                                                         = 2.π.r (h + r)