A cylinder is a closed solid shape with two parallel bases generally circular in shape connected by two parallel sides. A cylinder may also be defined as a rectangle with circular bases. These circular bases are always parallel and congruent to one another.
A cylinder when unrolled gives a flattened look of a rectangle. Base and sides together form a cylinder. The line joining the two circular bases at the center is the axis of the cylinder. Height (h) as seen in the figure is the perpendicular distance between the two bases. Each base has a radius (r).
Curved Surface area:
the length of the cylinder = the circumference of the base = 2πr. The breadth of the rectangle = Height of the cylindrical can = h.
Now, since the rectangular paper was used to wrap the Can firmly, we know that area of rectangle = area of the curved surface of the Cylindrical Can = l × b = 2πr × h
The Curved Surface Area of the Cylinder = 2πrh
We already know that a cylindrical shape is a combination of two circular bases and rectangle like shape that joins the two bases. So, the total surface area of this geometrical figure shall include the area of the two bases and the curved surface area.
Hence, the total surface area =
Area of base 1 +Area of base 2+ Curved surface area
`= πr^2 +πr^2 + 2πrh`
`= 2πr^2 + 2πrh `
= 2πr (r+h).
Thus,The Surface Area of a Cylinder = 2πr (r+h)
A company packages its milk powder in cylindrical container whose base has a diameter of 14 cm and height 20 cm. Company places a label around the surface of the container (as shown in the figure). If the label is placed 2 cm from top and bottom, what is the area of the label.
A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How much sheet of metal is required?
A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.
Rukhsar painted the outside of the cabinet of measure 1 m × 2 m × 1.5 m. How much surface area did she cover if she painted all except the bottom of the cabinet?
Find the curved surface area and total surface area of a cylinder, the diameter of whose base is 7 cm and height is 60 cm.