RIGHT CIRCULAR CYLINDER- MEANING, FORMULAE AND ILLUSTRATION

Every one of you has purchased a beverage can from the shop. Have you ever thought of the shape of that can? The shape of the can is like a right circular cylinder. There are many examples in our surroundings that have a cylindrical shape. So, In this article, we are going to learn about the meaning and formation of the right circular cylinder, its properties, its surface area & volume, some real-life examples and illustrations.

RIGHT CIRCULAR CYLINDER

MEANING OF RIGHT CIRCULAR CYLINDER

A right circular cylinder is formed by rotating a rectangle about one of its sides as an axis. It is a three-dimensional solid that consists of 2 parallel circular bases that are connected by a closed circular surface in which every base is in the form of a circular disk and each of the circular bases has a similar radius and are parallel to each other. The line passing through the middle of the right circular cylinder is called the axis and the axis of the cylinder conjoins the middle of the 2 circular bases of the cylinder. The perpendicular distance between both the circular bases is called the height of the right circular cylinder, which is represented by “h” in the given figure. The distance from the centre of the circular bases towards its outer boundary is called the radius, which is represented by “r” in the given figure.

PROPERTIES OF RIGHT CIRCULAR CYLINDER

1) The line that joins the circular base from the centre is the axis.

2) If a plane cuts the right circular cylinder horizontally parallel to the bases, then the intersection is a circle.

3) To specify a right circular cylinder, we need to know only its radius and its height.

4) The axis forms 90 degrees with circular bases.

SURFACE AREA OF RIGHT CIRCULAR CYLINDER

The surface space of a right circular cylinder is the total area lined by the surface of it. There are 2 types of surface areas of a right circular cylinder-:

1. Lateral or Curved surface area

It is the area of the cylinder excluding the areas of its circular bases. When the cylinder is opened from both ends then the curved surface area is calculated.

Formula

Curved surface area (CSA) = Circumference of circular base × height

                                               = 2πr × h

                                               = 2πrh sq. units.

2. Total surface area

It is the area covered by its curved surface and the two circular bases. When the cylinder is closed from both ends then the total surface area is calculated.

Formula

Total surface area (TSA) = Curved surface area + 2(Area of a circle)

                                           = 2πrh + 2πr²

                                           = 2πr(h+r) sq. units.

VOLUME AND FORMULA

It is the measure of the space occupied by the whole cylinder. The quantity is measured in cubic units.

Formula

Volume = Area of the circular disks x Height of the right circular Cylinder

               = πr² × h

               = πr²h cubic units

FORMATION OF A RIGHT CIRCULAR CYLINDER

When a rectangle is revolved about one of its sides, it forms the right circular cylinder. So, for the formation of a right circular cylinder, we need a rectangular sheet.

We will follow various steps for learning the formation of a right circular cylinder-

STEP 1 – We will take a rectangular sheet as given in the figure.

STEP 2 – Now, we will fold the rectangular sheet along with one of its sides(length) until the other two sides(breadth) merge.

STEP 3 – You will observe that after folding, the shape that is formed is a right circular cylinder. The length of the rectangle is equal to the circumference of the circular base and the breadth of the rectangle is equal to the height of the cylinder. The curved or lateral surface area of the cylinder is equal to the area of a rectangle,

Where length = 2πr = Circumference of the circular base(where r is the radius of the base.)

and breadth = h.

The curved surface area of cylinder = 2πrh = length(l)×breadth(b) = area of rectangular sheet used

ILLUSTRATIONS

Q1.  The radius of the base of the solid right circular cylinder is 10 cm and has a height of 20 cm. What’s its total surface area?

Sol.-

Total surface area = 2πrh + 2πr²

                                 =2πr(h + r)

                                 =2× 3.14×10(20 + 10)

                                 = 1885.71 cm².

Q2. What is going to be the quantity of a right circular cylinder, if the radius of the base is 20 centimetres and the height of the cylinder is 30 centimetres. (Given π= 3.14)

Sol.- 

Volume of a right cylinder = πr² h

                                               = 3.14 × 20² × 30

                                               = 3.14 × 400 × 30

                                               = 37680 cm³