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We learn about numerous solid shapes in Geometry, such as the cylinder, cube, cuboid, cone, etc,. A three-dimensional shape is the hollow cylinder. A hollow cylinder is a cylinder that is hollow on the inside and has some thickness on the outside. The surface of a hollow cylinder is established by a point at a specified distance from a certain line segment. The cylinder is one of the most fundamental curvilinear geometric structures, and it has two radii: R is the exterior or outside radius, and r is the inside or internal radius.
We will study the volume of a hollow cylinder.
Volume of hollow cylinder: –
The three-dimensional space enclosed by a hollow cylinder is defined as its volume. The volume of glass, for example, indicates the amount of space available within it. In other words, volume indicates the greatest amount of space that water can occupy if poured into a glass.
A hollow cylinder is one that is hollow on the inside and has a difference in radius between its internal and external radius. To put it another way, it’s a cylinder that’s hollow on the inside and has some thickness around the edges. An annular ring is the shape created at the bottom of a hollow cylinder, which is defined as a region surrounded by two concentric circles.
Formula of volume of hollow cylinder: –
A 3D shape with a circular base is known as a cylinder. A cylinder is made up of circular discs that are placed on top of one another. A hollow cylinder, on the other hand, is defined as a cylinder with an internal radius that differs from the outward radius.
With both the outer and inner radius of a hollow cylinder known, the volume may be calculated as follows:
V = π(R^2 – r^2) h cubic units is the volume of a hollow cylinder.
Where,
R = radius of outer cylinder.
r= radius of inner cylinder.
h = the hollow cylinder’s height.
Derivation of the volume of hollow cylinder:-
The formula for calculating a cylinder’s volume is as follows:
A cylinder’s volume is equal to its base area plus its height, which is equal to π(R^2) h cubic units.
Where,
R = cylinder’s radius.
h= Cylinder height
The volume of a hollow cylinder with an outer radius of ‘R’ and an inner radius of ‘r’ is equal to the volume of a solid cylinder with a radius of ‘R’ and a height of ‘h’ minus the volume of a solid cylinder with a radius of ‘r’ and a height of ‘h’.
As a result, the volume of a hollow cylinder equals the volume of the external cylinder minus the volume of Internal cylinder.
Now,
Volume of hollow cylinder =πR^2 h –πr^2h
= π(R^2 – r^2) h cubic units.
Hence , the volume of the hollow cylinder is π(R^2-r^2)h cubic units.
Where,
R = radius of outer cylinder.
r=radius of inner cylinder.
h= the hollow cylinder’s height.
Steps to find the volume of hollow cylinder:-
We can use the procedures below to compute the volume of a hollow cylinder with a given outer radius, ‘R,’ inner radius, ‘r,’ and height, ‘h.’
Step 1:Make a list of the hollow cylinder’s known dimensions and double-check that they are in the same units.
Step 2: Calculate the volume of a hollow cylinder using the formula: Volume of hollow cylinder = π(R^2 – r^2) h
Where,
R = radius of outer cylinder.
r= radius of inner cylinder.
h = the hollow cylinder’s height.
Step 3: Use units to represent the solution.
Conclusion:-
A hollow cylinder is one that is hollow on the inside and has a difference in radius between its internal and external radius. To put it another way, it’s a cylinder that’s hollow on the inside and has some thickness around the edges.
As a result, the volume of a hollow cylinder equals the volume of the external cylinder minus the volume of Internal cylinder.
the volume of hollow cylinder is:-
Volume =π(R^2 – r^2) h
Where,
R = radius of outer cylinder.
r= radius of inner cylinder.
h= the hollow cylinder’s height.
