Right Circular Cylinder

If we take a number of circular sheets of paper and stack them up what we get is a right circular cylinder. Since it has been kept at right angles to the circular base it is called a right circular cylinder. A right circular cylinder is a 3D shape with the circular bases at the ends. The circular bases have the same radius and are parallel to each other. All the points on the circular base are at a fixed distance from the straight line called the axis of the cylinder. The right circular cylinder is the most commonly used geometric figure. Example: A cold drink can, a gas cylinder, etc.


Right Circular Cylinder Definition

Right circular cylinder definition states that-

A cylinder whose base is a circle is called a circular cylinder. If the axis of the cylinder is perpendicular to its base then the cylinder is called a right circular cylinder. From the below figure segment AB is the axis of the cylinder it joins the centre of the two bases of the cylinder. 


The oblique cylinder is another type of cylinder, which does not have parallel bases, it resembles a tilted structure.

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Properties of Right Circular Cylinder

  • The line joining the centres of the circular base is called the axis of the right circular cylinder.

  • If a plane cuts the right cylinder horizontally parallel to the bases, then the shape we get is a circle.

  • The section obtained on cutting a right circular cylinder by a plane, which contains two elements and parallels to the axis of the cylinder is the rectangle.

  • When we revolve a rectangle about one side as the axis of revolution, a right cylinder is formed.


Formulas for Right Circular Cylinder

Some important terms used in the formulas for right circular cylinder are:

  • Base: Each of the circular ends of a right circular cylinder is called its base.

  • Axis: The line segment joining the centers of two circular bases and is perpendicular to the base of the right circular cylinder is called the axis of the right circular cylinder.

  • Radius(r): The radius is referred to as the radius of the circular base.

  • Height(h): the length of the axis of the cylinder is called the height of the cylinder. The perpendicular distance between the circular bases is referred to as the height of the right circular cylinder.

  • Lateral Surface: The curved surface between the two bases of a right circular cylinder which joins the bases is called its lateral surface.


Now let us study the formulas for total surface area of right circular cylinder, curved or lateral surface area, and volume of a right circular cylinder.

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Curved Surface Area

The curved surface joining the two bases of a right circular cylinder is called its lateral surface. The formula for the Lateral Surface Area or Curved Surface Area is given by 


Lateral or Curved Area = 2 \[\pi\] rh sq.units

Where.

r = radius of the circular base

h = height of the right circular cylinder 

\[\pi\]= 3.14 or \[\frac{22}{7}\]


Total Surface Area

The sum of the lateral surface area or curved surface area and the base areas of both the circles will give the total surface area of a right circular cylinder. The formula for the total surface area of the right circular cylinder(TSA) is given by


TSA = 2 \[\pi\] r (h + r) sq.units

Where.

r = radius of the circular base

h = height of the right circular cylinder 

\[\pi\] = 3.14 or \[\frac{22}{7}\]


Volume

The volume of the right circular cylinder is the product of any of the areas of the top or bottom circle and the height of the cylinder. The volume of the right circular cylinder is measured in terms of cubic units. The formula for the volume of a right circular cylinder is given by

The volume of Right Circular Cylinder(V)  = Area of the circular base ✕ Height of the Right Cylinder


Volume(V) = \[\pi\]\[r^{2}\]h


Solved Examples

Example 1: The curved surface area of a right circular cylinder of height is 88 \[cm^{2}\]. The height of the cylinder is 7cm. Find the radius and of the base of the cylinder.

Solution:

Let r be the radius and h be the height of the cylinder. Then,

The curved surface area of right circular cylinder = 2 \[\pi\]r h = 88

h = 14cm

2 \[\pi\] r h = 88

2 x \[\frac{22}{7}\]x r x 7 = 88 (\[\pi\] = \[\frac{22}{7}\])

44r = 88

r = 88/44

r = 2cm

Diameter = 2r

    = 2 x 2

    = 4cm

So the radius and diameter of the right circular cylinder are 2cm and 4cm respectively.


Example 2: Find the volume of a right circular cylinder, if the radius and height of the cylinder are 10cm and 15cm respectively.

Solution:

Given that, r = 10 cm h = 15 cm

Volume of a right circular cylinder = \[\pi\]\[r^{2}\]h 

Volume = 3.14 × \[10^{2}\] × 15

= 3.14 × 10 × 10 × 15

= 314 x 15

=4710 \[cm^{3}\].

Therefore the volume of the right circular cylinder is 4710 cubic centimeters.


Quiz Time

  1. An iron pipe 20cm long has a circular base diameter of 25cm. Find the surface area of the pipe.

  2. Find the total surface area and the volume of a cylindrical tin of radius 17 cm and height 3 cm.

FAQ (Frequently Asked Questions)

1. What is the Right Circular Cone?

Answer:

Right Circular Cone can be defined as, 

A right circular cone is a solid generated by revolving a line segment that passes through a fixed point and which makes a constant angle with a fixed-line.

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Here you see a right circular cone with ‘h’ is the height of the cone, ‘r’ is the radius of the cone, and L is the slant height of the cone.

2. What is the difference between Cylinder and Right Circular Cylinder?

Answer: Cylinder and Right Circular Cylinder are a similar shape with a slight difference in the inclination angle of the axis with the base. Some of the differences are:

  • The line segment joining the centers of two circular bases perpendicular to the base of the right circular cylinder is called the axis of the right circular cylinder.

  • While in a regular cylinder the axis of the cylinder can have any inclination with the circular base.

  • Also, the cross-section of a right circular cylinder is a rectangle or a square while of a regular cylinder, it is a parallelogram.