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