![]() ![]() Therefore, total surface area of the cylinder = 2πr 2 + 2πrh = 2πr(r + h)ĭifferences Between TSA and CSA of Cylinder.Thus, the area of this rectangle (l × b) is = 2πr × h = 2πrh which is also the curved surface area of the cylinder.In the rectangle, one side is the height of the cylinder h, while the length of this rectangle is the circumference of the circle, that is, 2πr.Now, the area of the two circles is (πr 2 + πr 2) whose base radius is 'r'.Observe the figure given above in which the area of the curved surface opens up as a rectangle and the two bases are circles. Let us open a cylinder in the 2-dimensional form and understand this. Consider the cylinder given below whose height is 'h' and radius is 'r'. A cylinder has 2 flat surfaces which are circles and a curved surface that opens up as a rectangle. The area of any shape is the space occupied by it. The more detailed and geometrical derivation of TSA of a cylinder is below. Solution: The total surface area (TSA) of a cylinder can be calculated using the formula, TSA = 2πr(r + h).īy substituting the values of r = 5, h = 8, we get: Thus, the total surface area of the cylinder (TSA) = πr 2 + πr 2 + 2πrh = 2πr 2 + 2πrh = 2πr (r + h).Įxample: Find the total surface area (TSA) of a cylinder of radius 5 cm and height 8 cm. Thus, the curved surface area of cylinder = 2πrh. Then the area of a rectangle is nothing but the area of the curved surface which is length × width = 2πr × h = 2πrh. Its width is nothing but the height of the cylinder 'h' and its length is the circumference of the base which is 2πr (to observe this, just close the rectangle back to the cylinder). We can see that the cylindrical shape is turned into a rectangle. Then cut the remaining cylindrical part vertically (height-wise) and open it. Take a coke tin and cut its top and bottom (we are cutting as we are just finding the "curved" surface area) faces. ![]() But how to find the area of the curved surface? For this, let us try a small experiment.We know that the area of each base (circle) has an area of πr 2.Total surface area of cylinder = Area of two bases + Area of the curved surface. Thus, the formula for the total surface area of the cylinder is given as, Consider a cylinder whose base has a radius 'r' and height of the cylinder is 'h'. The total surface area of the cylinder (TSA of cylinder) is obtained by adding the area of the two bases and the area of the curved surface. ![]()
0 Comments
Leave a Reply.AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |