Volume of a Cylinder

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Volume of a Cylinder

Volume Of Cylinder Definition

The volume of a cylinder means the space inside the cylinder that can hold a specific amount of material quantity.  In short, it is the capacity of the cylinder to hold solid, liquid, or gas  as it relates to volume. In order to understand the Capacity of Cylinder, it must be in a three-dimensional shape. It is not possible to measure the volume of two-dimensional cylinder.

Cylinder’s volume is given by the formula, ?r2h, where r is the radius of the circular base and h is the height of the cylinder.

Definition of a Cylinder

A cylinder is a three-dimensional shape that consists of two parallel bases linked by a curved surface. The line that  passes  from the center or joining the centers of two circular bases is referred to as the axis of the cylinder

What is the unit for the volume of a cylinder?

The volume of a cylinder is typically measured in what are called cubic units. These cubic units are generally displayed as follows:  cubic centimeters (cm3), cubic meters (m3), cubic feet (ft3). 

Types of Cylinders as it relates to Volume: 

  1. Oblique cylinder – A cylinder where both sides lean over the base at an angle that is not equal to a right angle, or 90 degrees.
  2. Elliptic cylinder – It is a cylinder whose bases are ellipses. Ellipses are curved lines.
  3. Right circular hollow cylinder – It has the shape of a right circular cylinder. However, it does not have closed circles.
  4. Right Cylinder –  A cylinder that has a closed circular surface having two parallel bases on both the ends and whose elements are perpendicular to its base.

Volume of a Right Circular Cylinder

The base of a right circular cylinder is a circle, which means the  the area of the circle of radius ‘r’ is ?r2. Thus, the volume (V) of a right circular cylinder, using the above formula, is,

V = ?r2h

Based on the above formula,

  • ‘r’ is the radius of the base of the cylinder
  • ‘h’ is the height of the cylinder
  • ? is a constant whose value is either 3.142.

Therefore, the volume of cylinder varies based on it height and directly varies with the square of its radius.

Volume of an Oblique Cylinder

In order to calculate the volume of an Oblique Cylinder, you will utilize the same formula as that of a right cylinder. The Volume (V)  of an oblique cylinder whose base radius is ‘r’ and whose height is ‘h’ is as follows: V = ?r2h

Volume of an Elliptic Cylinder

It is important to note that an ellipse has two radii. If we know that the area of an ellipse whose radii are ‘a’ and ‘b’ is ?ab.  The volume of an elliptic cylinder is: V = ?abh

To break this down further,

  • ‘a’ and ‘b’ are the radii of the base of the cylinder.
  • ‘h’ is the height of the cylinder.
  • ? is a constant whose value is 3.142.

Volume of a Right Circular Hollow Cylinder

A right circular cylinder is a shape that has two right circular cylinders – one inside the other. In order to obtain the volume, you must subtract  the volume inside cylinder from the volume of the outside cylinder. Therefore, the volume (V) formula  for a Right Circular Hollow Cylinder is as follows: ,

V = ?(R2 – r2)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.
  • ? is a constant whose value is 3.142.

Steps to calculate the volume of a cylinder

The below steps will provide you with process of finding the volume of a cylinder.

Step 1: Identify the type of cylinder given to you in the question or in real life.  Is the cylinder a right cylinder, an oblique cylinder,  Right Circular Hollow Cylinder, or an elliptic cylinder?

Step 2: Once you have decided on the type of cylinder, you will need to figure out the formula that is best used for the associated Cylinder.

      • Right Cylinder:  V = ?r2h
      • Oblique Cylinder:  V = ?r2h
      • Elliptic Cylinder: V = ?abh
      • Right Circular Hollow Cylinder: V = ?(R2 – r2)h

Step 3: Make sure you verify that you have all dimensions needed, and they are utilizing the same unit of measurement.

Step 4: Simply match the units with their appropriate variable in the formula, and solve the formula.

Below you will find a simple example for a Right Cylinder utilizing Area and Height.

Result

V = ? a^2 h (for a circular right cylinder with center at the origin, height h, radius a)

Example plots

Example plots

Equation

x^2 + y^2<=a^2 and -h/2<=z<=h/2

Solid properties

0

h

S = 2 ? a (a + h)

S_L = 2 ? a h

x^_ = (0, 0, 0)

I = (1/12 (3 a^2 + h^2) | 0 | 0 0 | 1/12 (3 a^2 + h^2) | 0 0 | 0 | a^2/2)

Distance properties

max(2 a, sqrt(4 a^2 + h^2))

? = 1

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