. Surface Area Surface area is the measurement of all exposed area of a solid object. . .
Right Circular Cylinder Observe the given figures in Fig. . and identify the shape. These objects resemble the shape of a cylinder.
Definition : A right circular cylinder is a solid generated by the revolution of a rectangle about one of its sides as axis. If the axis is perpendicular to the radius then the cylinder is called a right circular cylinder. In the Fig. .
, AB = h represent the height and AD = r represent the radius of the cylinder. A solid cylinder is an object bounded by two circular plane surfaces and a curved surface. The area between the two circular bases is called its ‘Lateral Surface Area’ (L.S.A.) or ‘Curved Surface Area’ (C.S.A.). Formation of a Right Circular Cylinder – Demonstration (i) Take a rectangle sheet of a paper of length l and breadth b .
(ii) Revolve the paper about one of its sides, say b to complete a full rotation (without overlapping). (iii) The shape thus formed will be a right circular cylinder whose circumference of the base is l and the height is b . Fig. .
Drum Pipe Tube Light D h Fig. . Fig. .
Top circular base Lateral (or) Curved surface Bottom circular base Fig. . l l l Mensuration Surface Area of a Right Circular Cylinder (i) Curved surface area Curved surface area (C.S.A.) of a right circular cylinder = Area of the corresponding rectangle = × l p r h ( l is the circumference = p rh of the base, b is the height)[see Fig. .
] C.S.A. of a right circular cylinder = p rh sq. units. (ii) Total surface area Total surface area refers to the sum of areas of the curved surface area and the two circular regions at the top and bottom.
That is, total surface area (T.S.A.) of right circular cylinder = C.S.A + Area of top circular region +Area of bottom circular region. rh r (Refer Fig. . ) rh p r h T.S.A.
of a right circular cylinder = p r h ) sq. units Example . A cylindrical drum has a height of cm and base radius of cm. Find its curved surface area and the total surface area.
Solution Given that, height of the cylinder h = cm ; radius r = cm Now, C.S.A. of the cylinder = p rh sq. units C.S.A. of the cylinder = = × × = cm T.S.A.
of the cylinder = p r h r sq. units = cm Therefore, C.S.A. = cm and T.S.A. = cm