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Mathemaitcs
**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 + 2πr^{2 }= 2πr(h + r )

(iii) Volume =Area of cross section × Height = πr^{2}h

**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 = *R* – *r*

(ii) Area of Cross - section = π(R^{2 }− r^{2})

(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^{2 }− r^{2}) = 2π(Rh + rh + R^{2 }− r^{2} )

(vi) Volume of the material = πR^{2}h − πr^{2}h = π(R^{2 }− r^{2})h.