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Right circular cylinders are one of the most common solid figures used in mathematics. A right circular cylinder has two circular ends and a curved surface joining the circular ends. Like a cube, cuboid, sphere, and many other shapes, a right circular cylinder is a three-dimensional solid figure.
- Both the ends of the right circular cylinder are parallel to each other, and they are characterised with a closed circular curved surface.
- The right circular cylinder has an imaginary line running through the center of the cylinder, joining both the circular surfaces; this imaginary line is known as the axis.
- The distance between each point on the closed circular surface of a right circular cylinder and the cylinder's axis is constant.
- A right circular cylinder has three parameters which can be calculated, total surface area, curved surface area, and the volume of the cylinder.
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Key Terms: Right circular cylinder, curved surface area, total surface area, volume, curved surface area
Right Circular Cylinder
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A right circular cylinder is a common cylindrical solid figure. It has two circular bases that are parallel to one another. The right circular cylinder is a three dimensional structure. The two bases of the cylinder are joined at their centers by the cylinder's axis. The cylinder's axis is an imaginary line running through the center of the cylinder, joining the two bases. The right circular cylinder consists of three parts:
- Circular top base,
- Sideways curve surface, and
- Circular face at bottom
Right Circular Cylinder
Parts of a Right Circular Cylinder
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A right circular cylinder comprises of the following parts:
- Base: It is known as the circular ends of a right circular cylinder. One right circular cylinder has two bases, one at the top, and one at the bottom.
- Axis: It's the line segment that runs perpendicular to the base of the right circular cylinder and joins the centers of two circular bases. The axis is an imaginary vertical line.
- Radius: Radius refers to the straight line from the center of the base, to it circumference, and it is represented by r
- Height: The length of the cylinder's axis is known as it's height and it is represented by h.
Properties of a Right Circular Cylinder
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The properties of the right circular cylinder are listed below:
- The axis is the vertical line that runs through the center of the cylinder and connects the centers of the top face and bottom face.
- The curved surface of the right angle cylinder is a rectange.
- When a right angle cylinder is cut across the axis, the two dimensional shape obtained on the plane is a rectangle
- When a right angle cylinder is cut horizontally across the base, the two dimensional shape obtained on the plane is a circle
- An ideal right circular cylinder has two edges.
- There are no vertices present in a right circular cylinder.
- The bases of cylindrical structures are parallel to each other
- When a rectangle is rotated using one side as the axis of revolution, then a right cylinder is formed
- The formula for a cylinder's longest diagonal is d2 = 4r2 + h2.
Formulas for Right Circular Cylinder
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There are three main formulas for the right circular cylinder. The three formulas are listed below:
Curved surface area of right circular cylinder
A right circular cylinder has two types of surface areas, total and curved. The curved surface area, is the area only comptising of the curved surface, which means, excluding the two circular bases. Hence the curved surface area is:
Curved surface area of right circular cylinder = 2πrh
Where,
r = radius of the cylinder
h = height of the right circular cylinder
Example: Find the curved surface area of a right cylinder, if the radius is 13 cm and height is 40 cm. (Take pi as 22/7)
Solution. To calculate the curved surface area,
Radius r = 13cm
Height h = 40 cm
CSA = 2πrh
CSA = 2 X π X 13 X 40
CSA = 3268.57 cm2
Total surface area of right circular cylinder
The total surface area of the right circular cylinder is calculated by adding the area of both the top and the bottom circles, to the curved surface area.
Curved surface area of right circular cylinder = 2πrh
Area of two circles = 2πr2
Total surface area of right circular cylinder = 2πrh + 2πr2 = 2πr(h+r)2
Where,
r = radius of the cylinder
h = height of the right circular cylinder
Example: Find the total surface area of a right cylinder, if the radius and height of the cylinder are 1 cm and 3 cm respectively.
Ans. To calculate the total surface area,
Radius r = 1cm
Height h = 3 cm
TSA = 2πr(h+r)2
TSA = 2 X π X 1 X (3 + 1)2
TSA = 50.24 cm2
Volume of right circular cylinder
Volume of the right circular cylinder refers to the solid space the cylinder occupies. The area of the top or bottom circle multiplied by the height of the cylinder gives the volume of a right circular cylinder. Right cylinder volumes are expressed in terms of cubic units.
Volume of right circular cylinder = πhr2
Where,
r = radius of the cylinder
h = height of the right circular cylinder
Example: Find the volume of a right cylinder, if the radius and height of the cylinder are 1 cm and 4 cm respectively.
Solution: To calculate the volume,
Radius r = 1 cm
Height h = 4 cm
Volume = πhr2
Volume = π X 4 X 1 X 1
Volume = 12.57 cm2
Volume of right circular cylinder
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Things to Remember
- A cylinder with circular bases that are parallel to one another is the right circular cylinder.
- A right circular cylinder is a three dimensional structure
- A right cylinder is created when a rectangle is rotated around one side as the axis of revolution.
- The right circular cylinder consists of three parts: Circular bases at top and bottom, and Sideways curve surface.
- Formula for Curved surface area of right circular cylinder is 2πrh
- Formula for total surface area of right circular cylinder is 2πr(h+r)2
- The axis is the vertical line that connects the circle's centers.
- Formula for volume of right circular cylinder is πhr2
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Sample Questions
Ques. Find the volume of a right cylinder, if the radius and height of the cylinder are 10 cm and 40 cm respectively. (2 marks)
Ans. To calculate the volume,
Radius r = 10cm
Height h = 40 cm
Volume = πhr2
Volume = π X 40 X 10 X 10
Volume = 12,571.42 cm2
Ques. Find the total surface area of a right cylinder, if the radius and height of the cylinder are 10 cm and 30 cm respectively. (2 marks)
Ans. To calculate the total surface area,
Radius r = 10cm
Height h = 30 cm
TSA = 2πr(h+r)2
TSA = 2 X π X 10 X (30 + 10)2
TSA = 1,00,571.4 cm2
Ques. Find the volume of a right cylinder, if the radius and height of the cylinder are 15 cm and 35 cm respectively. (2 marks)
Ans. To calculate the volume,
Radius r = 15cm
Height h = 35 cm
Volume = πhr2
Volume = π X 35 X 15 X 15
Volume = 25750 cm2
Ques. Write 5 properties of a right angle cylinder (5 marks)
Ans. A right angle cylinder has the following properties:
- The axis is the vertical line that connects the circle's centers.
- A right cylinder is created when a rectangle is rotated around one side as the axis of revolution.
- The rectangle is the portion that results from cutting a right circular cylinder with a plane that has two components and runs parallel to the cylinder's axis.
- A circle is formed when a plane cuts the right cylinder horizontally and parallel to the bases.
- An ideal right circular cylinder has two edges.
Ques. Find the curved surface area of a right cylinder, if the radius and height of the cylinder are 20 cm and 40 cm respectively. (2 marks)
Ans. To calculate the curved surface area,
Radius r = 10 cm
Height h = 30 cm
CSA = 2πrh
CSA = 2 X π X 10 X 30
CSA = 1884 cm2
Ques. The radius and height of a right cylinder are given as 6 m and 7.5 m respectively. Find the volume and total surface area of the right cylinder. (3 marks)
Ans. To calculate the volume and TSA,
Radius r = 6 m
Height h = 7.5 m
Volume = πhr2
Volume = π X 7.5 X 6 X 6
Volume = 847.8 m2
TSA = 2πr(h+r)2
TSA = 2 X π X 6 X (7.5 + 6)2
TSA = 6867.18 cm2
Ques. Write down the components of a right angle cylinder (3 marks)
Ans. A right circular cylinder comprises of the following parts:
- Base: It is known as each of the circular ends of a right circular cylinder.
- Axis: It's the line segment that runs perpendicular to the base of the right circular cylinder and joins the centers of two circular bases.
- Radius: This term denotes the radius of the circular base, which is represented by r
- Height: The cylinder's axis length is indicated by this measurement, which is represented by h.
Ques. The radius and height of a right cylinder are given as 8 m and 10.5 m respectively. Find the volume and total surface area of the right cylinder. (3 marks)
Ans. To calculate the volume and TSA,
Radius r = 8 m
Height h = 10.5 m
Volume = πhr2
Volume = π X 10.5 X 8 X 8
Volume = 6625.65 m2
TSA = 2πr(h+r)2
TSA = 2 X π X 8 X (10.5 + 8)2
TSA = 17194.18 cm2
Ques. The radius and height of a right cylinder are given as 10 m and 10.5 m respectively. Find the volume and curved surface area of the right cylinder. (3 marks)
Ans. To calculate the volume and TSA,
Radius r = 10 m
Height h = 10.5 m
Volume = πhr2
Volume = π X 10.5 X 10 X 10
Volume = 7625.65 m2
CSA = 2πr(h+r)2
CSA = 2 X π X 10 X (10.5 + 10)2
CSA = 17184.18 cm2
Ques. The radius and height of a right cylinder are given as 7 m and 10.5 m respectively. Find the volume and curved surface area of the right cylinder. (3 marks)
Ans. To calculate the volume and TSA,
Radius r = 7 m
Height h = 10.5 m
Volume = πhr2
Volume = π X 10.5 X 8 X 8
Volume = 6625.65 m2
CSA = 2πr(h+r)2
CSA = 2 X π X 8 X (10.5 + 8)2
CSA = 17194.18 cm2
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