Volume of a Hollow Cylinder (original) (raw)
Last Updated : 23 Jul, 2025
A cylinder is a three-dimensional object that is formed when a rectangle is rotated along any of its sides. A hollow cylinder is one type of cylinder that is hollow from the inside. A hollow cylinder can be defined as a three-dimensional geometric object that is empty from the inside. A hollow cylinder consists of two circular bases that have inner and outer radii. The circular bases are similar to an annular ring, which is a region bounded by two concentric circles.
**Hollow Cylinder
A cylinder, which is empty from the inside and has some difference between the internal and external radius is called as H. We can see some thickness enclosed between the inner radius and the outer radius, which is equal to the difference between the internal and external radius. The height, or altitude, of the hollow cylinder, is the perpendicular distance between its two circular bases. Straws, water pipes, tubes, toilet paper rolls, etc. are some examples of hollow cylinders that we see in our daily lives.
Volume of Hollow Cylinder Formula
The three-dimensional space enclosed by a hollow cylinder is referred to as its volume. For example, the maximum space that can be occupied by oil when the oil is poured into a cylindrical glass jar is the volume of the jar. Now, the formula to calculate the volume of a hollow cylinder is given as follows:
**Volume of Hollow Cylinder = π(R 2 -r 2 )h cubic units
where,
"**h" is the height of the hollow cylinder,
"**R" is the outer radius of the given cylinder, and
"**r" is the inner radius of the given cylinder.
Volume of Hollow Cylinder Derivation
We know that the formula to calculate the volume of a solid cylinder when radius (r) and height (h) is (πr2)h cubic units.
**Volume of cylinder = Base area × Height = (πr 2 )h cubic units
Now, the volume of a hollow cylinder is equal to the difference between the volume of the external cylinder and the volume of the internal cylinder.
Let us consider that the outer radius of the hollow cylinder is "R," its inner radius is "r," and "h" is the height of the cylinder.
Volume of a hollow cylinder = (Volume of the cylinder with outer radius "R" and height "h") – (Volume of the cylinder with inner radius "r" and height "h")
Volume of a hollow cylinder (V) = πR2 × h – πr2 × h
**V = π(R 2 -r 2 )h cubic units
How to Find the Volume of Hollow Cylinder?
Let’s take an example to understand how to calculate the volume of a hollow cylinder.
**Example: Calculate the volume of a hollow cylinder whose external radius is 12 cm, the internal radius is 9 cm, and the height is 7 cm
**Solution:
**Step 1: Note the values of the given dimensions. Here, the external radius (R) is 12 cm, the internal radius (r) is 9 cm, and the height (h) is 7 cm.
**Step 2: We know that the formula to find the volume of a hollow cylinder is [π × (R2−r2) × h] cubic units. Now, substitute the given values in the formula.
**Step 3: Thus, the volume of a hollow cylinder is calculated as
**V = (22/7) × (12 2 - 9 2 ) × 7
**V = 1,386 cm 3
Solved Examples on Volume of Hollow Cylinder
**Example 1: Calculate the volume of a hollow cylinder whose external radius is 10 cm, the internal radius is 5 cm, and the height is 8 cm [Use π= 22/7]
**Solution:
External Radius (R) = 10 cm
Internal Radius (r) = 5 cm
Height (h) = 8 cm
We know that,
The volume of a hollow cylinder = π × (R2−r2) × h cubic units
= (22/7) × (102 - 52) × 8
= (22/7) × 75 × 8
= 1,885.714 cm3Hence, the volume of the given hollow cylinder is 1,885.714 cm3
**Example 2: Calculate the volume of a hollow cylinder whose external radius is 12 inches, the internal radius is 8 inches, and the height is 6 inches. [Use π= 22/7]
**Solution:
External Radius (R) = 12 inches
Internal Radius (r) = 8 inches
Height (h) = 6 inches
We know that,
The volume of a hollow cylinder = π × (R2 -r2) × h cubic units
= (22/7) × (122 - 82) × 6
= (22/7) × 80 × 6
= 1,508.571 in3Hence, the volume of the given hollow cylinder is 1,508.571 in3
**Example 3: Determine the volume of a hollow cylindrical tube whose thickness is 4 m, the internal radius is 5 m, and the height is 8 m. [Use π= 22/7]
**Solution:
Internal Radius (r) = 5 m
The thickness of the cylindrical tube = 4 m
t = R - r = 4 m
R - 5 = 4
R = 4 + 5 = 9 m
Height (h) = 8 m
We know that,
The volume of a hollow cylinder = π × (R2 -r2) × h cubic units
= (22/7) × (92 - 52) × 8
= (22/7) × 56 × 6 = 1,408 m3Hence, the volume of the given hollow cylinder is 1,408 m3
**Example 4: Calculate the height of a hollow cylinder whose outer diameter is 16 cm, the inner diameter is 12 cm, and the volume is 792 cm 3 . [Use π= 22/7]
**Solution:
Outer diameter = 16 cm
So, External Radius (R) = 16 cm/ 2 = 8 cm
Inner diameter = 12 cm
So, Internal Radius (r) = 12 cm/2 = 6 cm
Height = ?
We know that,
Volume of a hollow cylinder = π × (R2 -r2) × h cubic units
792 = (22/7) × (82 - 62) × H
H = 9Hence, the height of hollow cylinder is 9 cm