#2608. Surface area of a cylinder

Mathematics, level: Middle
Posted Sun Jun 9 07:32:52 PDT 2002 by Mrs. Narinder Jeet Makkar (robinmakkar@yahoo.com).
Salwan Public School, New Delhi, India
Materials Required: cylinder made up of thick paper with detachable bases, scissors, ordinary classroom equipment
Activity Time: 40 minutes
Concepts Taught: area of curved surface and total surface area of a cylinder

The students are shown a cylinder made up of thick sheet and its shape is discussed i.e. its curved surface and its circular bases. The two important parameters of a cylinder are discussed -- the first is the radius of its circular cross section and second the height of a cylinder.
The students are asked to remove the circular disc from the circular cylinder with the help of scissor. If 'r' be the radius of the cylinder, then the students are able to tell the area of the circular top and circular base (area of the top = area of base = ðr2).
Next, the students are asked to cut the curved surface along its height with the help of scissors. They are able to identify the shape obtained which is a rectangle. They are able to tell the breadth of the rectangle (it is the same as the height of the cylinder 'h'). The students are then asked to tell the length of the rectangle. The length of the rectangle is the same as the circumference of the circular base (i.e. 2ðr). Now the students are able to derive the formula for the curved surface area of the cylinder (2ðrh).
They are asked to find the total surface area of the cylinder. They add the area of the curved surface and the area of the two circular bases to obtain the formula for the total surface area of the cylinder. This way the students are able to understand and remember the formulas.