Hollow Cylinder is one of the top three dimensional cylinders in solid figures. A hollow cylinder consists of two cylinders in it. From the top view of the shape, we can see two circles. let us discuss what is meant by the hollow cylinder and its formulas from this article. The measurement of the hollow cylinder can be done by finding the surface area, lateral surface area and volume of the hollow cylinder. For a deep explanation regarding the hollow cylinder, we suggest you go through the entire article.
What is meant by Hollow Cylinder?
A hollow cylinder is a type of cylinder. It is empty from the outside and it has a difference in the outer surface radius and inner surface radius of a cylinder. It also has a different inner lateral surface area and outer lateral surface area and it also has different inner and outer radii.
Volume of Hollow Cylinder Formula
The volume of a hollow cylinder is nothing but the capacity that a shape can hold. The formula to calculate the volume of a hollow cylinder is shown below.
Volume of hollow cylinder = volume of external cylinder – volume of internal cylinder = πh(R² – r²)
Where
R = radius of the outer surface
r = radius of the inner surface
Surface area of a Hollow Cylinder Formula
The area of the hollow cylinder can be measured in terms of surface area and lateral surface area. It is nothing but the area covered by the hollow cylinder. Check out the formula given below to solve the problems on the surface area of the hollow cylinder.
Surface area of a hollow cylinder = lateral surface area + area of solid bases = 2πh(R + r) + 2π(R² – r²)
R = radius of the outer surface
r = radius of the inner surface
Lateral surface area of a hollow cylinder = external surface area of a cylinder + internal surface area of a cylinder = 2πh(R + r)
R = radius of the outer surface
r = radius of the inner surface
Also, See:
Hollow Cylinder Examples
Example 1.
Find the volume of a hollow cylinder having inner radius = 3 cm, outer radius = 8 cm and height = 7 cm.
Solution:
Given that
Inner radius of the hollow cylinder (r) = 3 cm
Outer radius of the hollow cylinder (R) = 8 cm
Height of the hollow cylinder (h) = 7 cm
Volume of the given hollow cylinder = π (R²- r²) h
= (22/7)((8)² – (3)²(7)
= 22(64 – 9)
= 55 cm³
Volume of the hollow cylinder is 55 cm³
Example 2.
A hollow cylinder copper pipe is 21dm long. Its outer diameter and inner diameters are 12cm and 4cm respectively. Find the volume of copper used in manufacturing the pipe.
Solution:
Given that,
The height of the cylindrical pipe is h = 21dm =210cm
External radius, R = 12/2=6cm
Internal radius, r = 4/2=2cm
The volume of the copper used in manufacturing the pipe = Volume of external cylinder−volume of an internal cylinder
= πR²h−πr²h
= π(R²−r²)h
= 22/7[5²−4²]×210
=22/7 × 32 ×210
= 22× 32 ×30
= 21130 cu. cm
Example 3.
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, the 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
external radius R = 6 + 2 = 8 m
The cylindrical surface area of the cylindrical tunnel = the cylindrical surface area of the hollow cylinder.
the cylindrical surface area of the hollow cylinder = 2π(R + r)h sq. units
Where π = 22/7
= 2 × (22/7) (8 + 6)×25
= 2200 m²
The cylindrical surface area of the cylindrical tunnel is 2200 m²
Area covered by one litre of paint = 10 m²
The number of litres required to paint the tunnel = 2200/10 = 220
Therefore, 220 litres of paint is needed to paint the tunnel
Example 4.
Find the volume of a hollow cylinder having inner radius = 4 cm, outer radius = 8 cm and height = 6 cm.
Solution:
Given that
Inner radius of the hollow cylinder (r) = 4 cm
Outer radius of the hollow cylinder (R) = 8 cm
Height of the hollow cylinder (h) = 6 cm
Volume of the given hollow cylinder = π (R²- r²) h
= (22/7)((8)² – (4)²(6)
= 22/7(64 – 16) (6)
=904.33 cm³
The volume of the hollow cylinder is cm³
Example 5.
The lateral surface area of a hollow cylinder is 422 cm². It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of the rectangular sheet.
Solution:
The hollow cylinder is converted into a rectangular sheet
So, the area of the cylinder and sheet must be the same
The curved surface area of hollow cylinder = area of the rectangular sheet
422 = length × breadth
422 = l × 33
422/33 = l
l = 12.7
Perimeter of sheet = 2( l + b)
= 2(12.7 + 33)
= 78.7 cm
FAQs on Hollow Cylinder
1. What is the difference between a hollow cylinder and a cylinder?
A solid-surface produced by a line moving parallel to a fixed line, while its end describes a closed figure in a plane is called a cylinder. A cylinder is the limiting case of a prism. The difference is that a hollow cylinder consists of two radii internal and external radius and the cylinder consists of only one radius.
2. What is a hollow cylinder called?
A hollow cylinder is also called a tube.
3. What is the formula of the area of the hollow cylinder?
The inner curved surface area = 2πr × Height, the outer curved surface area = 2πR × Height.