Cylinder


Cylinder

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

 = 2πrh

(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

Hollow Cylinder

Let R and r be the external and internal radii of a hollow cylinder, and h be its height, then

(i) Thickness of Cylinder = Rr

(ii)  Area of Cross - section = π(R− 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(R− r2) = 2π(Rh + rh + R− r2 )

(vi) Volume of the material = πR2h − πr2h = π(R− r2)h.