write the formula to find the total surface area of cylinder band explain the term in it
Answers
TSA = 2π × r × h + 2πr2= 2πr (h + r) Square.Let us take a cylinder of base radius ‘r’ and height ‘h’ units. The curved surface of this cylinder, if opened along the diameter (d=2r) of the circular base can be transformed into a rectangle of length ‘2πr’ and height ‘h’ units. ThusBy the formula of area of the circle, we know,
Area of circular base of cylinder = πr2
Since, there are two circular bases, therefore area of both the circular bases = πr2+πr2 = 2πr2.
Now, from the figure you can see, when we open the curved surface of the cylinder in two-dimension space, it forms a rectangle. Hence, the height and circumference of the circular bases are the dimensions of the rectangle formed from it. Therefore,
Area of the curved surface = Height x Circumference
Curved Surface area = h x πd = h x 2πr ( d = 2r)
CSA = 2πrh …………….(2)
By adding equation 1 and equation 2, we get the total surface area, such that;
Total Surface area = Curved Surface area + Area of Circular bases
TSA = 2πrh + 2πr2
By taking 2πr as common factor from RHS, we get;
TSA = 2πr (h + r)
This is the formula for the total surface area of a given cylinder whose radius is r and height is h.
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Answer:
TSA +-#;-#-2-222+2+2+