Volume of a Cylinder
Before learning the definition and the formula to find the volume of a cylinder, let us recall what is a cylinder first. A cylinder is a threedimensional shape with two congruent and parallel identical bases. There are different types of cylinders. They are:
 Right circular cylinder: A cylinder whose bases are circles and each line segment that is a part of the lateral curved surface is perpendicular to the bases.
 Oblique cylinder: A cylinder whose sides lean over the base at an angle that is not equal to a right angle.
 Elliptic cylinder: A cylinder whose bases are ellipses.
 Right circular hollow cylinder: A cylinder that consists of two right circular cylinders bounded one inside the other.
1.  Volume of a Cylinder 
2.  Volume of a Cylinder Formula 
3.  How To Calculate the Volume of a Cylinder? 
4.  FAQs on Volume of a Cylinder 
Volume of a Cylinder
The volume of a cylinder is the number of unit cubes (cubes of unit length) that can be fit into it. It is the space occupied by the cylinder as the volume of any threedimensional shape is the space occupied by it. The volume of a cylinder is measured in cubic units such as cm^{3}, m^{3}, in^{3}, etc. Let us see the formula used to calculate the volume of a cylinder.
Volume of a Cylinder Formula
We know that a cylinder resembles a prism (but note that a cylinder is not a prism as it has a curved side face), we use the same formula of volume of a prism to calculate the volume of a cylinder as well. We know that the area of a prism is calculated using the formula,
V = A × h, where
 A = area of the base
 h = height
Now we will apply this formula to calculate the volume of each type of cylinder.
Volume of a Right Circular Cylinder
We know that the base of a right circular cylinder is a circle and the area of a circle of radius 'r' is πr^{2}. Thus, the volume (V) of a right circular cylinder, using the above formula, is,
V = πr^{2}h
Here,
 'r' is the radius of the base (circle) of the cylinder
 'h' is the height of the cylinder
 π is a constant whose value is either 22/7 (or) 3.142.
Thus, the volume of a cylinder directly varies with its height and directly varies with the square of its radius. i.e., if the radius of the cylinder becomes double, then its volume becomes four times.
Volume of an Oblique Cylinder
The formula to calculate the volume of an oblique cylinder is the same as that of a right circular cylinder. Thus, the volume (V) of an oblique cylinder whose base radius is 'r' and whose height is 'h' is,
V = πr^{2}h
Volume of an Elliptic Cylinder
We know that an ellipse has two radii. Also, we know that the area of an ellipse whose radii are 'a' and 'b' is πab. Thus, the volume of an elliptic cylinder is,
V = πabh
Here,
 'a' and 'b' are the radii of the base (ellipse) of the cylinder.
 'h' is the height of the cylinder.
 π is a constant whose value is either 22/7 (or) 3.142.
Volume of a Right Circular Hollow Cylinder
As a right circular cylinder is a cylinder that consists of two right circular cylinders bounded one inside the other, its volume is obtained by subtracting the volume of the inside cylinder from that of the outside cylinder. Thus, the volume (V) of a right circular hollow cylinder is,
V = π(R^{2 }– r^{2})h
Here,
 'R' is the base radius of the outside cylinder.
 'r' is the base radius of the inside cylinder.
 'h' is the height of the cylinder.
 π is a constant whose value is either 22/7 (or) 3.142.
How To Calculate the Volume of a Cylinder?
Here are the steps to calculate the volume of a right circular cylinder.
 Identify the radius to be 'r' and height to be 'h' and make sure that they both are of the same units.
 Substitute the values in the formula V = πr^{2}h.
 Write the units as cubic units.
Example: Find the volume of a right circular cylinder of radius 50 cm and height 1 meter. Use π= 3.142.
Solution:
The radius of the cylinder is, r = 50 cm.
Its height is, h = 1 meter = 100 cm.
Its volume is, V = πr^{2}h = (3.142)(50)^{2}(100) = 785,500 cm^{3}.
Note: We need to use the formula to find the volume of a cylinder depending on its type as we discussed in the previous section. Also, assume that a cylinder is a right circular cylinder if there is no type given and apply the volume formula to be V = πr^{2}h.
Solved Examples on Volume of a Cylinder

Example 1: Find the volume of a cylindrical water tank whose base radius is 25 inches and whose height is 120 inches. Use π = 3.14.
Solution:
The radius of the cylindrical tank is, r = 25 inches.
Its height is, h = 120 inches.
Using the volume of a cylinder formula, the volume of the tank is,
V = πr^{2}h
V = (3.14)(25)^{2}(120) = 235500 cubic inches.
Answer: The volume of the given cylindrical tank is 235,500 cubic inches.

Example 2: Find the volume of an elliptic cylinder whose base radii are 7 inches and 10 inches, and whose height is 15 inches. Use π = 22/7.
Solution:
The base radii of the given elliptic cuboid are,
a = 7 inches and b = 10 inches.
Its height is, h = 15 inches.
Using the volume of a cylinder formula, the volume of the given elliptic cylinder is,
V = πabh
V = (22/7) × 7 × 10 × 15 = 3300 cubic inches.
Answer: The volume of the given cylinder is 3,300 cubic inches.
FAQs on Volume of a Cylinder
What Is the Volume of a Cylinder?
The volume of a cylinder is the amount of space in it. It can be obtained by multiplying its base area by its height. The volume of a cylinder of base radius 'r' and height 'h' is V = πr^{2}h.
What Is the Formula for Volume of a Cylinder?
The formula for the volume of a cylinder is V = πr^{2}h, where
 'r' is the radius of the base of the cylinder
 'h' is the height of the cylinder
 π is a constant whose value is either 22/7 (or) 3.142.
What Is the Volume of a Cylinder With Diameter?
Let us consider a cylinder of radius 'r', diameter 'd', and height 'h'. The volume of a cylinder of base radius 'r' and height 'h' is V = πr^{2}h. We know that r = d/2. By substituting this in the above formula, V = πd^{2}h/4.
What Is the Ratio of the Volume of a Cylinder and a Cone?
Let us consider a cylinder and a cone, each with base radius 'r' and height 'h'. We know that the volume of the cylinder is πr^{2}h and the volume of the cone is 1/3 πr^{2}h. Thus the required ratio is 1 : (1/3) (or) 3 : 1.
How To Find Volume of a Cylinder With Diameter and Height?
The volume of a cylinder with base radius 'r' and height 'h' is, V = πr^{2}h. If its base diameter is d, then we have d = r/2. Substituting this in the above formula, we get V = πd^{2}h/4. Thus, the formula to find the volume of a cylinder with the diameter (d) and height(h) is V = πd^{2}h/4..
How To Find Volume of a Cylinder With Circumference and Height?
We know that the circumference of a circle of radius 'r' is C = 2πr. Thus, when the circumference of the base of a cylinder (C) and its height (h) are given, then we first solve the equation C = 2πr for 'r' and then we apply the volume of a cylinder formula, which is, V = πr^{2}h.
How To Calculate Volume of a Cylinder in Litres?
We can use the following conversion formulas to convert the volume of a cylinder from m^{3} (or) cm^{3} to liters.
 1 m^{3} = 1000 liters.
 1 cm^{3} = 1 ml (or) 0.001 liters.
What Happens to the Volume of Cylinder When Its Radius Is Halved?
The volume of a cylinder directly varies with the square of its radius. Thus, when its radius is halved, the volume becomes 1/4^{th}.