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A cylinder is a solid three-dimensional form made up of two parallel bases connected by a curved surface. These bases are shaped like a round disc.
- Properties of cylinder explain the attributes of a Three Dimensional Geometry.
- The axis of the cylinder is a line that runs from the centre or connects the centres of two circular bases.
- Height, "h," represents the distance between the two-cylinder bottoms, which is known as perpendicular distance.
- The radius, denoted by "r," is the distance between the centre and the outer limit of the two circular bases.
- Cylinder is made up of two circles and one rectangle.
- Cold drink cans and tissue paper rolls are some real-life examples of cylinders.
- The important formulas of the cylinder are as follows:
TSA = 2πr(h+r) square units
CSA = 2πrh square units
V= πr²h cubic units.
Key Terms: Properties of cylinder, Cylinder, Surface Area, Volume, Curved surface area, Elliptical cylinder, Inclined Cylinder, Right Circular Cylinder, Oblique Cylinder, Radius, Height
Types of Cylinder
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We just read about several real-life cylinder examples, demonstrating that cylinders come in a variety of shapes and sizes. There are four different types of cylinders in geometry. They are as follows:
Right Circular Cylinder
A right circular cylinder is made by rolling a rectangle on one of its sides to create an axis. The cylinder is called a right circular cylinder if the axis (one of the rectangle's sides) is perpendicular to the radius (r).
- The cylinder's base and top are both circular and parallel to each other.
- The distance between these circular faces is known as the cylinder's height (h).
Example of Right Circular CylinderExample: Find the curved surface area of a right cylinder, if the radius is 14 cm and height is 20 cm. (Take pi as 22/7) Solution. To calculate the curved surface area, Radius r = 14cm Height h = 20 cm CSA = 2πrh CSA = 2 X π X 14 X 20 CSA = 1760 cm2 |
Oblique Cylinder
The sides of an oblique cylinder lean over the base. The sides of an oblique cylinder are not perpendicular to the base's center.
Example of Oblique CylinderExample: The Leaning Tower of Pisa is an example of an oblique cylinder in real life. |
Elliptic Cylinder
An elliptic cylinder is a cylinder whose base is shaped like an ellipse.
Cylindrical Shell
The right circular hollow cylinder, also known as a "cylindrical shell," is made up of two right circular cylinders, one of which is bounded inside the other.
- The axis has a common point that is perpendicular to the central base.
- It differs from the right circular cylinder in that it is hollow inside, meaning there is some space or void.
Cylinder
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Properties of the Cylinder
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Every geometrical shape has its unique qualities or properties that set it apart from the others. A cylinder, too, has a few features that describe it.
- The cylinder's bases are always congruent and parallel to one another.
- A "right cylinder" is one in which the axis of the cylinder forms a right angle with the base.
- The bases are exactly one above the other.
- An "inclined cylinder" is one in which one of the cylinder bases is shown on the side.
- In this, axis does not form a straight angle to the sockets.
- It's called a right circular cylinder if the bases are circular.
- An ellipse is the finest alternative to a cylinder's circular basis.
- It's called an "elliptical cylinder" when the bottom of the cylinder is elliptical.
- A circular cylinder is formed when a line moves parallel to and at a set distance from the axis.
- A cylinder, like a prism, has the same cross-section all the way around.
Cylinder Formulas
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The important cylinder formulas are as follows:
- Total Surface Area of a Circle
2πrh + 2πr² = 2πr(h+r) square units
- Curved Surface Area, C.S.A
2πrh square units
πr²h cubic units.
- The area of the cylinder's side face is 2πrh square units.
Example of Cylinder FormulasExample: Find the volume of the cylinder with a radius of 7 cm and a height 7 cm? Solution: Given: Radius, r = 7 cm Height, h = 7 cm Volume of the cylinder, V = πr2h cubic units. V = (22/7) x 72 x 7 V = 22 x 49 V= 1078 Cubic units. Example: Find the curved surface area of a right cylinder, if the radius is 14 cm and height is 14 cm. (Take pi as 22/7) Solution. To calculate the curved surface area, Radius r = 14cm Height h = 14 cm CSA = 2πrh CSA = 2 X π X 14 X 14 CSA = 1232 cm2 |
Read More:
| Chapter Relevant Concepts | ||
|---|---|---|
| Remainder Theorem | Eccentricity of an Ellipse | Triangles |
| Similarities of Triangle | Pythagoras Theorem | Semicircle |
Things to Remember
- A cylinder is like a prism that has the same cross-section all the way around.
- The base of a cylinder has two circles that are at a specific distance from each other, referred to as height.
- If bases of a cylinder are circular it is called a right circular cylinder.
- The cylinder's base and top are identical, i.e. they have the same round or elliptical base.
- Properties of cylinder will describe unique qualities about the figure.
- Gas cylinders and road rollers are all examples of cylinders.
Sample Questions
Ques. Britt wants to buy a can that can hold 1 gallon of oil. The radius of the can is 5 inches. Help Britt find the height of the can she has to buy. Hint: The can is in the form of a cylinder. (3 marks)
Ans. Volume V= 1 gallon
1 gallon= 231 cubic inches
Radius r = 5 inches
The volume of a cylinder V = ????r2h
231 = 22/7 × (5)² × h
(231 × 7)/(22 × 25) = h
h = 2.94 inches.
Therefore, the height of the can should be 2.94 inches.
Ques. What is the volume of a cylindrical shape water container, that has a height of 7cm and a diameter of 10cm. (3 marks)
Ans. Given,
Diameter of the container = 10cm
Thus, the radius of the container = 10/2 = 5cm
Height of the container = 7cm
As we know, from the formula,
The volume of a cylinder = πr²h cubic units.
Therefore, volume of the given container, V = π × 52 × 7
V = π × 25 × 7 = (22/7) × 25 × 7 = 22 × 25
V = 550 cm³
Ques. Find the lateral surface area when the radius of the cylinder is 10cm and height is 20cm. Use π=3.14 (2 marks)
Ans. The formula of lateral/ curved surface area of a cylinder is 2πrh. Thus,
2πrh=2×3.14×10×20cm²=1256cm²
Hence, the lateral surface area of the cylinder is 1256cm².
Ques. Find the volume of a cylindrical shaped oil container that has a height of 8cm and a diameter of 12cm. Use π=3.14 (3 marks)
Ans. Given, Diameter of the container =12cm
Thus, the radius of the container =12/2cm=6cm
Height of the container =8cm
The formula of the volume of a cylinder =πr²h cubic units.
Therefore, the volume of the given container =π(6)2×8cm³
Volume =3.14×(62)×8cm³=904.32cm³
Hence, the volume of the cylinder is 904.32cm³.
Ques. The volume of a cylindrical water tank is 1000m³ and the height of the tank is 20m. Calculate the radius of the tank. Use π=3.14. (2 marks)
Ans. Given: Height (h) of base =20m and volume of tank =1000m³
We know that volume of a cylinder =πr²h
So, 1000=3.14×r²×20
r=√15.92=3.99≈4m
Hence, the radius of the tank is 4m (approximately).
Ques. Find the volume of a cylindrical metal pipe, whose length is 40cm and the outer radius is 80cm, and the thickness of the metal pipe is 2cm. Use π=3.14 (3 marks)
Ans. Given
Length (h) of the metal pipe =40cm
The outer radius of the pipe =80cm
The inner radius of the pipe = Outer radius of the pipe − Thickness of the
metal pipe
The inner radius of the pipe =(80–2)cm=78cm
We know that volume of a hollow cylinder =π(R2–r2)h
Now, the volume of a metal pipe =3.14×(802–782)×40=39689cm³.
Hence, the volume of a metal pipe is 39689.6cm³
Ques. Emma has an old cylindrical water tank at her home. The radius is 40 inches and the height is 150 inches. She wants to replace it with a new one with the same dimensions. Help Emma figure out the area of the water tank. (2 marks)
Ans. The water tank is in the form of a cylinder.
Total Surface Area of a cylinder = 2 x 22/7 xr(h+r)
TSA = 2 × 22/7 × 40(150 + 40)
TSA = 2 × 22/7 × 7600
TSA = 47,771.42 sq.inches
Area of the water tank = 47,771.42 sq.inches.
Ques. What is the volume of the cylinder with a radius of 5 units and a height of 8 units. (3 marks)
Ans. Radius,r = 5 units
Height,h = 8 units
Volume of the cylinder, V = πr2h cubic units.
V = (22/7) × 52 × 8
V = 22/7 × 25 × 8
V= 628.57 Cubic units.
Therefore the volume of the cylinder is 628.57 cubic units.
Ques. Find the lateral surface area when the radius of the cylinder is 50cm and height is 40cm. Use π=3.14 (2 marks)
Ans. The formula of lateral/ curved surface area of a cylinder is 2πrh. Thus,
2πrh=2×3.14×50×40cm²=12560cm²
Hence, the lateral surface area of the cylinder is 12560cm².
Ques. Find the volume of a cylindrical shaped oil container that has a height of 14 cm and a diameter of 14cm. Use π=3.14 (3 marks)
Ans. Given, Diameter of the container =14cm
Thus, the radius of the container =14/2cm=7cm
Height of the container =14 cm
The formula of the volume of a cylinder =πr²h cubic units.
Therefore, the volume of the given container =π(7)2×14cm³
Volume =3.14×(72)×14cm³=2154.04cm³
Hence, the volume of the cylinder is 2154.04cm³.
Ques. The volume of a cylindrical water tank is 1000m³ and the height of the tank is 140m. Calculate the radius of the tank. Use π=3.14. (2 marks)
Ans. Given: Height (h) of base =140m and volume of tank =1000m³
We know that volume of a cylinder =πr²h
So, 1000=3.14×r²×140
r=√2.27=1.50≈2m
Hence, the radius of the tank is 2m (approximately).
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