HOW TO SOLVING VOLUME OF CYLINDER

 

Volume of Cylinder

The volume of a cylinder is the capacity of the cylinder which calculates the amount of material quantity it can hold. In geometry, there is a specific formula to calculate the volume of a cylinder that is used to measure how much amount of any quantity whether liquid or solid can be immersed in it uniformly. A cylinder is a three-dimensional 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.

The formula to find the volume of a cylinder is V = πr²h. Let us learn more about this formula in the upcoming sections.

 

What is the 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 three-dimensional shape is the space occupied by it. The volume of a cylinder is measured in cubic units such as cm3, m3, in3, etc. Let us see the formula used to calculate the volume of a cylinder.

 

Definition of a Cylinder

A cylinder is a three-dimensional solid shape that consists of two parallel bases linked by a curved surface. These bases are like a circular disk in a shape. The line passing from the center or joining the centers of two circular bases is called the axis of the cylinder.

 

Volume of 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 volume of a prism is calculated using the formula,

 

V = A × h

 

where

A = area of the base

h = height

Using this formula, the formulas of volume of cylinder are:

The formula for volume of a right circular cylinder is,

V = πr²h (r = radius, h = height)

The formula for volume of an oblique cylinder is,

V = πr²h (r = radius, h = height)

The formula for volume of an elliptic cylinder is,

V = πabh (a and b = radii, h = height)

The formula for volume of a right circular hollow cylinder is,

V = π(R² - r²)h (R = outer radius, r = inner radius, h = height)

 

Now we will apply the formula V = A × h to calculate the volume of different types of cylinders.

 

Volume of a Right Circular Cylinder Formula

We know that the base of a right circular cylinder is a circle and the area of a circle of radius 'r' is πr². Thus, the volume (V) of a right circular cylinder, using the above formula (V = A × h), is,

V = πr²h

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 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.

 

Formula to Find Volume of an Oblique Cylinder

The formula to calculate the volume of cylinder (oblique) 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 = πr²h

 

Formula to Calculate 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 Formula

As a right circular hollow 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(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.

π is a constant whose value is 22/7 (or) 3.142.

 

How To Find the Volume of Cylinder?

Here are the steps to find the volume of 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 volume formula V = πr²h.

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 = πr²h = (3.142)(50)²(100) = 785,500 cm³.

 

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 of a cylinder formula to be V = πr²h.

 

Important Notes on Volume of Cylinder:

The volume of a cylinder is calculated using the formula, V = πr²h, where r is the radius of its circular base and 'h' is the perpendicular distance (height) between the centres of the bases.

If diameter (d) is given, then find the radius (r) using r = d/2 and then substitute in the above formula to find the volume of cylinder.