An object bounded by two co-axial cylinders of the same height and different radii is called a ‘hollow cylinder’.

Surface Area

Surface area is the measurement of all exposed area of a solid object.

**Hollow Cylinder**

An object bounded by two co-axial cylinders of the same height and
different radii is called a ‘hollow cylinder’.

Let *R* and *r* be the outer and inner radii of the
cylinder. Let *h* be its height.

C.S.A of the hollow cylinder = outer C.S.A. of the cylinder + inner
C.S.A. of the cylinder

= 2πRh +2πrh

C.S.A of a hollow cylinder = 2*π*(*R* + *r*)*h*
sq. units

T.S.A. of the hollow cylinder = C.S.A. + Area of two rings at the
top and bottom.

= 2*π*(*R* + *r*)*h*
+ 2*π*(*R*^{2} −*r*^{2})

T.S.A. of a hollow cylinder = 2*π*(*R* + *r*)(*R*
− *r* + *h*) sq. units

** **

If one litre of paint covers 10 m^{2}, how many litres of
paint is required to paint the internal and external surface areas of a
cylindrical tunnel whose thickness is 2 m, internal radius is 6 m and
height is 25 m.

Given that, height* **h*** **= 25

internal radius *r* = 6 m

Now, external radius *R* = 6 + 2 = 8 m

C.S.A. of the cylindrical tunnel = C.S.A. of the hollow cylinder

C.S.A. of the hollow cylinder = 2*π*(*R* + *r*)*h*
sq. units

= 2 × (22/7) (8 + 6)×25

Hence, C.S.A. of the cylindrical tunnel = 2200 m^{2}

Area covered by one litre of paint = 10 m^{2}

Number of litres required to paint the tunnel = 2200/10 = 220 .

Therefore, 220 litres of paint is needed to paint the tunnel.

** **

1. Right circular cylinder is a solid obtained by revolving
_______ about _______.

2. In a right circular cylinder the axis is _______to the
diameter.

3. The difference between the C.S.A. and T.S.A. of a right
circular cylinder is ______.

4. The C.S.A. of a right circular cylinder of equal radius and
height is ________ the area of its base.

** **

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10th Mathematics : UNIT 7 : Mensuration : Surface Area: Hollow Cylinder | Definition, Formula, Solved Example Problems | Mensuration | Mathematics

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