The area of the curved surface of the cylinder, excluding the areas of the two circular bases. The sum of the areas of all the surfaces of the cylinder, including the two circular bases and the curved surface. The following table best summarizes the differences between TSA and CSA of a cylinder. The main difference between the Total Surface Area (TSA) and the Curved Surface Area (CSA) of a Cylinder is that TSA is the sum of the areas of all the surfaces of the cylinder, including the two circular bases and the curved surface, while CSA is the area of the curved surface only. 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'. Formulas to find the area in square yards are provided for measurements given in yards or feet to simplify conversion.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. The following formulas show how to calculate area in square yards for various shapes. Sq yds = (length ft × width ft) ÷ 9 Formulas to Find Square Yards Multiply the length in feet times the width in feet to find the area in square feetĭivide the area by 9 to find square yards. Follow these steps if all of your measurements are in feet: The steps above guide you to convert all measurements to yards before multiplying, but it’s possible to find square yards after multiplying if all of your measurements are in feet too. Sq yds = length yds × width yds How to Find Square Yards Using Measurements in Feet Multiply the length times the width to get the area measurement in sq yds. Measure the length and width of each side of the rectangleĬonvert these measurements to yards as described above. Use these steps to calculate the area of a rectangular space in square yards. Diagram demonstrating that 1 square yard is equal to a 3 ft x 3 ft square, or 9 sq ft.
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