A solid obtained by revolving a rectangular lamina about one of its sides is called a right circular cylinder.
(i) The radius of any circular cross-section is called the radius of the cylinder.
(ii) The Line joining the centre of circular cross-section at the end is called the axis of the cylinder.
(iii) The distance between the centre of circular cross-section at the end is called the height or length of the cylinder.
Let r be the radius and h be the height of a solid cylinder, then
(i) Curved surface area
= Perimeter of cross-section × Height
(ii) Total surface area
= Curved surface area + Area of two circular ends
=2πrh + 2πr2 = 2πr(h + r )
(iii) Volume =Area of cross section × Height = πr2h
Let R and r be the external and internal radii of a hollow cylinder, and h be its height, then
(i) Thickness of Cylinder = R – r
(ii) Area of Cross - section = π(R2 − r2)
(iii) External curved surface area =2πrh
(iv) Internal curved surface area = 2πrh
(v) Total Surface Area
= External curved area + Internal curved area
+ Area of two ends
= 2πRh + 2πrh + 2π(R2 − r2) = 2π(Rh + rh + R2 − r2 )
(vi) Volume of the material = πR2h − πr2h = π(R2 − r2)h.