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Volume of Cylinder in Terms of Pi
The volume of a cylinder in terms of pi is the capacity of the cylinder which signifies the amount of any material it can hold or the amount of any material that can be immersed in it in terms of pi. The formula to calculate the cylinder’s volume is given as πr^{2}h, where r is the radius of the circular base and h is the height of the cylinder. The material could be any substance or any liquid quantity which can be filled in the cylinder uniformly.
1.  What is Volume of Cylinder in Terms of Pi? 
2.  Formula of Volume of Cylinder in Terms of Pi 
3.  How to Calculate Volume of Cylinder in Terms of Pi? 
4.  FAQs on Volume of Cylinder in Terms of Pi 
What is Volume of Cylinder in Terms of Pi?
The volume of the cylinder in terms of pi the capacity of the cylinder which is indicated in terms of pi. The cylinder is a threedimensional shape that has a circular base. A cylinder can be observed as a set of circular disks that are stacked on one another. The unit of volume of the cylinder in terms of pi is given in terms of cubic units, where the unit can be m^{3}, cm^{3}, in^{3}, or ft^{3}, etc.
Formula of Volume of Cylinder in Terms of Pi
A cylinder can be observed as a collection of multiple congruent disks, that are stacked one over the other. To calculate the space occupied by a cylinder, we find the total space occupied by each disk and then add them up. Therefore, the volume of the cylinder is given by the product of the area of base and height. For any cylinder whose base radius is "r", and height is "h", the volume will be base times its height. Therefore, the cylinder’s volume of base radius "r", and height "h" = (area of base) × height of the cylinder. Since the base is the circle, it can be written as Volume = πr^{2 }× h
How to Calculate Volume of a Cylinder?
The volume of a cylinder can be calculated by simply finding the space occupied by a cylinder. The volume of the cylinder is given by the product of the area of base and height. The volume of different types of the cylinder in terms of pi is explained below:
A cylinder can be categorized into different types based on its structure:
Right Circular Cylinder
If the axis of the two parallel lines is perpendicular to the center of the base, it is called the right circular cylinder.
The volume of a cylinder = Area of a circle × height
The volume of a right circular cylinder in terms of pi = πr^{2}h cubic units where r is the radius of the cylinder and h is the height of the cylinder.
Oblique Cylinder
An oblique cylinder is one whose sides lean over the base. In an oblique cylinder, the sides are not perpendicular to the center of the base. In general, the volume of an object is the base area along with its height. The heights and base area for oblique and right circular cylinders are the same. Therefore the volume of an oblique cylinder is the same as the volume of a right circular cylinder. The volume of the oblique cylinder in terms of pi = πr^{2}h cubic units where r is the radius of the cylinder and h is the height of the cylinder.
Elliptic Cylinder
A cylinder whose base is in the form of an ellipse is called an elliptic cylinder. The base of an elliptic cylinder is in the form of an ellipse. So, there are two radii "a", "b" and height is "h".
The volume of the elliptic cylinder in terms of pi = πabh cubic units where h is the height of the cylinder, a is the semimajor axis of the base of the cylinder, and b is the semiminor axis of the base of the cylinder.
Right Circular Hollow Cylinder (Cylindrical Shell)
The right circular hollow cylinder also called a "cylindrical shell", consists of two right circular cylinders bounded one inside the other. The point of the axis is common and is perpendicular to the central base. It is different from the right circular cylinder since it is hollow in nature, i.e. there is some space or void present inside. We know that volume of a cylinder = πr^{2}h In a cylindrical shell, we have two radii "R" and "r". Therefore, the volume of cylindrical shell = π(R^{2}–r^{2})h cubic units where "R" is the outer radius of the base of the cylinder and "r" is the inner radius of the base of the cylinder.
Solved Examples on Volume of Cylinder in Terms of Pi

Example 1: Find the height of the cylinder if the volume of the cylinder in terms of pi is 125π cubic inches and the radius of the cylinder is 5 inches.
Solution: Given that volume of the cylinder in terms of pi = 125π cubic inches and r = 5 inches.
The volume of a cylinder V = πr^{2}h cubic units
125π = π × (5)^{2 }× h
⇒ h = 125/25 = 5Answer: The height of the cylinder is 5 inches.

Example 2: Find the volume of the cylinder in terms of pi if the height of the cylinder is 140 inches and a base radius of 40 inches.
Solution: Given that h = 140 inches and r = 40 inches
We know, the volume of a cylinder, V = πr^{2}h cubic units
V = π × (40)^{2} × 140
⇒ V = 224000π in^{3}Answer: The volume of the cylinder in terms of pi is 224000π in^{3}.
FAQs on Volume of Cylinder in Terms of Pi
What is the Volume of Cylinder in Terms of Pi?
It is defined as the capacity of a cylinder which is indicated in terms of pi. The volume of a cylinder in terms of pi is expressed in cubic units where units can be m^{3}, cm^{3}, in^{3}, or ft^{3}.
What is the Formula To Calculate the Volume of the Cylinder in Terms of Pi?
The formula that is used to determine the volume of the cylinder in terms of pi is V = πr^{2}h cubic units where, "V", "r" and "h" are the volume, radius, and height of the cylinder. This formula of volume of the cylinder also shows its dependence on the radius and height of the cylinder.
How to Find the Volume of Cylinder in Terms of Pi?
We can find the volume of the cylinder in terms of pi using the following steps:
 Step 1: Identify the given dimensions of the radius and height of the cylinder.
 Step 2: Square the value of radius.
 Step 3: Multiply the obtained value to π and the height of the cylinder.
 Step 4: The obtained value is the volume of the cylinder in terms of pi which is written with cubic units in the end.
How to Find the Radius of Cylinder If the Volume of Cylinder in Terms of Pi is Known?
We can find the volume of the cylinder in terms of pi using the following steps:
 Step 1: Identify the given dimensions cylinder and let the radius of the cylinder is "r"
 Step 2: Square the value of radius.
 Step 3: Multiply the obtained value to π and the height of the cylinder.
 Step 4: Now solve for "r" from the aboveobtained equation
 Step 5: The obtained value is the radius of the cylinder which is written with units in the end.
What is the Formula for Volume of Cylinder in Terms of Pi If the Cylinder is Oblique?
An oblique cylinder is one whose sides lean over the base. In an oblique cylinder, the sides are not perpendicular to the center of the base. The heights and base area for oblique and right circular cylinders are the same. Therefore the volume of an oblique cylinder is the same as the volume of a right circular cylinder. The volume of the oblique cylinder in terms of pi = πr^{2}h cubic units where r is the radius of the cylinder and h is the height of the cylinder.
What is the Formula for Volume of Cylinder in Terms of Pi If the Cylinder is Elliptical?
A cylinder whose base is in the form of an ellipse is called an elliptic cylinder. The base of an elliptic cylinder is in the form of an ellipse. So, there are two radii "a" and "b", and height "h". The volume of the elliptic cylinder in terms of pi = πabh cubic units where h is the height of the cylinder, a is the semimajor axis of the base of the cylinder, and b is the semiminor axis of the base of the cylinder.
What is the Formula for Volume of Cylinder in Terms of Pi If the Cylinder is a Right Circular Hollow Cylinder?
The right circular hollow cylinder also called a "cylindrical shell", consists of two right circular cylinders bounded one inside the other. The point of the axis is common and is perpendicular to the central base. The volume of cylindrical shell = π(R^{2 }– r^{2})h cubic units where R is the outer radius of the base of the cylinder and r is the inner radius of the base of the cylinder.
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