Introduction

In our day-to day life ,we come across several solids like measuring jars,circular pillars,circular pipes,a garden roller,gas cylinder etc.These solids have a curved lateral surfaces with congruent circular ends. such solids are right circular cylinders

A Solid generated by the revolution of a rectangle about one of its sides is called a right circular cylinder

Base

Each of the circular ends on which the cylinder restsis calle a base

Axis

The line segment joining centres of two circular bases is called the axis of the base.

Radius

The radius of the circular bases is called the radius of the cylinder and is denoted by r.

Height

The length of the axis of cylinder is called the height of cylinder and is denoted by h

Lateral Surface

The curved surface joining the two bases of a right circular cylinder is called its lateral surface. lateral surface area is given by

L.S. A = 2rh sq. unit

 

Total Surface Area

The total surface area is the lateral surface area and area of its two bases

T.S. A = 2rh +2r²

= 2r(h + r) sq. units

 

Volume

The measure of the space occupied by cylinder is area of base x height

Volume = r²h cubic units

Hollow Cylinder

A solid bounded by two coaxial cylinders of the same height and different radii is called a hollow cylinder e.g. iron pipes,rubber tubes are example of hollow cylinders

If R and r be the external and internal radii of a hollow cylinder and h be the height then

1)Base Area = (R² - r²)sq. units

2) Curved Surface Area or Lateral Surface Area = (External surface area ) + ( Internal surface Area)

=2Rh + 2rh

= 2h(R + r) sq. units

3)Total Surface Area =2Rh + 2rh + 2(R² - r²)

=2 ( R + r)(h + R - r) sq. units

4) Volume of the material = Exterior Volume - Interior Volume

= R²h - r²h cubic units

= (R² - r²)h cubic units