Formula for the Volume of a Hollow Cylinder:-
Volume of a hollow cylinder- V = Ï€ (R² - r²) h cubic unitsVolume of hollow cylinder =
Ï€ R² h - Ï€ r² h = Ï€ (R² - r²) h cubic unitsVolume of a cylinder :-
Base area × Height = (Ï€ R²) × h cubic unitsVolume of Hollow Pipe Calculator
The volume of a hollow cylinder represents the three-dimensional space enclosed within its boundaries. This space, often referred to in everyday scenarios such as the volume of a glass, signifies the capacity available inside the hollow cylinder. Essentially, the volume indicates the maximum amount of material that can fill the space enclosed by the cylinder. In this discussion, we delve into the concept of a hollow cylinder, explore its formula for volume calculation, derive the formula, and elucidate a method for finding the volume through solved examples.
A hollow cylinder distinguishes itself from a solid cylinder by its inner emptiness and the disparity between its internal and external radii. Visually, it resembles a cylinder with a thickness at its periphery, devoid of any material within. The bottom shape of a hollow cylinder takes the form of an annular ring, delineated by two concentric circles. This section aims to expound on the volume of a hollow cylinder, augmented by practical examples.
Formula for the Volume of a Hollow Cylinder:-
A hollow cylinder comprises a circular base and extends three-dimensionally. Conceptually, one can envision a hollow cylinder as a series of circular disks stacked atop one another. The volume of such a hollow cylinder, given its outer radius R, inner radius r, and height h, is determined by the formula:
Volume of a hollow cylinder- V = Ï€ (R² - r²) h cubic units
Where:
- R denotes the outer radius,
- r signifies the inner radius, and
- h represents the height of the hollow cylinder.
Derivation of the Volume Formula:-
The volume of a solid cylinder, with radius R and height h, is calculated using the formula for the volume of a cylinder:
Volume of a cylinder = Base area × Height = (Ï€ R²) × h cubic units
By subtracting the volume of a solid cylinder with radius r from that with radius R, we obtain the volume of the hollow cylinder:
Volume of hollow cylinder = External cylinder volume - Internal cylinder volume
⇒ Volume of hollow cylinder = Ï€ R² h - Ï€ r² h = Ï€ (R² - r²) h cubic units
where:-
R = outer radius,
r = inner radius, and,
h = height of the hollow cylinder
Procedure to Find Volume of Hollow Cylinder:-
To ascertain the volume of a hollow cylinder with given dimensions R, r, and h, the following steps are followed:
1. Note down the known dimensions of the hollow cylinder, ensuring consistency in units.
2. Apply the formula for the volume of a hollow cylinder: Volume of hollow cylinder = Ï€ (R² - r²) h.
3. Express the result with appropriate units.
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Example 1:-
Find the volume of a hollow cylinder whose outer radius is 7 cm and inner radius is 5 cm and height is 7 cm. (Use π = 22/7)
Solution:
Given:
Outer Radius = 7 cm
Inner Radius = 5 cm
Height = 7 cm.
To find: Volume “V”.
We know that the formula for the volume of a hollow cylinder is π (R2-r2)h cubic units.
Substituting the known values in the formula, we get
V = (22/7)(72 – 52)7 cm3
V = 22(49-25) cm3
V = 22(24) cm3
V = 528 cm3
Therefore, the volume of a hollow cylinder’s outer radius is 7 cm,
inner radius is 5 cm and height is 7 cm is 528 cm3.
Example:
Example 1:-
Find the volume of a hollow cylinder whose outer radius is 7 cm and inner radius is 5 cm and height is 7 cm. (Use π = 22/7)
Solution:
Given:
Outer Radius = 7 cm
Inner Radius = 5 cm
Height = 7 cm.
To find: Volume “V”.
We know that the formula for the volume of a hollow cylinder is π (R2-r2)h cubic units.
Substituting the known values in the formula, we get
V = (22/7)(72 – 52)7 cm3
V = 22(49-25) cm3
V = 22(24) cm3
V = 528 cm3
Therefore, the volume of a hollow cylinder’s outer radius is 7 cm,
inner radius is 5 cm and height is 7 cm is 528 cm3.Let's illustrate the calculation of the volume of a hollow cylinder with an inner radius of 20 units, outer radius of 30 units, and height of 21 units, using π = 22/7:
Volume = Ï€ (R² - r²) h
= (22/7) (30² - 20²) × 21
= (22/7) (900 - 400) × 21
= (22/7) (500) × 21
= 110 × 500
= 55,000 cubic units
Thus, the volume of the given hollow cylinder is 55,000 cubic units.
By comprehending the formula and method delineated above, one can effortlessly determine the volume of any hollow cylinder. To reinforce this understanding, let's delve into a few solved examples in the subsequent section.