Right Circular Cylinder

A right circular cylinder is a type of cylinder having a closed circular surface with two parallel bases on both the ends. It is also called the right cylinder.

The line that passes through the center of the two parallel bases is called the axis. The distance between the two bases of the cylinder is the perpendicular distance called the height (h). The radius (r) of the right circular cylinder is the distance from the center to the outer boundary for either of the two bases.

Thus, a right circular cylinder is a combination of two circles and a rectangle as shown below:

Properties

1. Has 2 curved edges, 1 curved surface, and 2 flat faces
2. The 2 circular bases (top and bottom) always are congruent
3. The size depends on the radius and the height of the cylinder
4. The axis forms a right angle with the 2 bases
5. does not have any vertex or corner

Formulas

Volume

The volume of a right circular cylinder is the amount of space occupied by it in the three-dimensional shape. It is measured in cubic units such as m3, cm3, mm3, ft3.

The formula to calculate the volume of a right circular cylinder is given below:

Thus, the volume is directly proportional to the height and square of its radius.

Let us solve an example to understand the concept better.

Find the volume of a right cylinder, if the radius and height of the cylinder are 10 m and 15 m respectively.

Solution:

As we know,
Volume (V) = πr2h, here π = 3.141, r = 10 m, h = 15 m
= 3.141 × 10 × 10 × 15
= 4.7115 × 10m3

Surface Area

A cylinder has 2 types of surface areas. It is expressed in square units such as m2, cm2, mm2, and in2. The 2 types are named and described below.

Lateral (Curved) Surface Area

The lateral surface area (LSA) of a right circular cylinder is the area that is covered by the curved surface of the cylinder. It is the space between the parallel circular bases of the cylinder. The formula to calculate the LSA of a right circular cylinder is:

Total Surface Area

The total surface area (TSA) of a right circular cylinder is the area occupied by the entire cylinder. It includes the area of 2 circular bases and 1 curved surface. The formula to calculate the TSA of a right circular cylinder is given below:

Let us solve some examples to understand the concept better.

The radius and height of a right cylinder are given as 6 m and 7.5 m respectively. Find the curved surface area and total surface area of the cylinder.

Solution:

As we know,
Curved Surface Area (CSA) = 2πrh, here π = 3.141, r = 6 m, h = 7.5 m
= 2 × 3.141 × 6 × 7.5
= 282.69 m2
Next,
Total Surface Area (TSA) = 2πr(r + h), here π = 3.141, r = 6 m, h = 7.5 m
= 2 × 3.141 × 6(6 + 7.5)
= 37.692 × 13.5
= 508.842 m2

Find the lateral surface area of a right circular cylinder with a base circumference of 44 units and a height of 12 units.

Solution:

As we know,
The lateral surface area is the curved surface area of the cylinder
Curved Surface Area (CSA) = 2πrh, here 2πr = 44 units, h = 12 m
Since the above formula can be rewritten as:
Curved Surface Area (CSA) = Base circumference (2πr) × height (h)
= 44 × 12
= 528 square units
Thus, the lateral surface area of a right circular cylinder with a base circumference of 44 units and a height of 12 units is 528 square units

The radius of the base of a solid right circular cylinder is 6 cm and its height is 22 cm. Find its (i) volume, (ii) curved surface area, and (iii) total surface area.

Solution:

As we know,
Volume (V) = πr2h, here π = 3.141, r = 6 m, h = 22 m
= 3.141 × 6 × 6 × 22
= 24876 × 103 cm3
Next,
As we know,
Curved Surface Area (CSA) = 2πrh, here π = 3.141, r = 6 m, h = 22 m
= 2 × 3.141 × 6 × 22
= 829.224 cm2
Next,
Total Surface Area (TSA) = 2πr(r + h), here π = 3.141, r = 6 m, h = 22 m
= 2 × 3.141 × 6(6 + 22)
= 37.692 × 28
= 1055.376 cm2