Surface Area: Hollow Cylinder

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 = 2π(R + r)h sq. units

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

 = 2π(R + r)h  + 2π(R² −r²)

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

Example 7.4

If one litre of paint covers 10 m², 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.

Solution

Given that, height h = 25 m; thickness = 2 m.

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 = 2π(R + r)h sq. units

= 2 × (22/7) (8 + 6)×25

Hence, C.S.A. of the cylindrical tunnel = 2200 m²

Area covered by one litre of paint = 10 m²

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

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

Progress Check

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.