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The cylinder is an exciting figure. It is a three-dimensional solid object which includes two circular bases connected with a curved face. It has both surface area and volume due to its 3D structure. Our primary consciousness is to understand the idea of the surface area of the cylinder, to calculate the total surface area and the lateral surface area of a cylinder. It is represented in square units of centimeters and meters. The surface vicinity of a cylinder is defined as the entire area covered by the curved surface and flat surfaces of the base of a cylinder. It has two essential components:
- Curved surface area
- Two flat faces of the flat surface area.
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Keyterms: Solid, Cylinder, Curved surface, Vicinity, Circle, Radius, Angle, Base, Rectangle
Read Also: Surface Areas and Volumes Revision Notes
Definition
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The surface vicinity of a cylinder is the amount of space covered by the flat surfaces and the curved aspect of the cylinder. It is actually the sum of a vicinity of a circle (the base of the cylinder is a circle) and the vicinity of the curved surface is a rectangle lengthwise, the high point of the cylinder, and the circumference of the base as its width. The two circular bases are juxtaposed over each other in a right cylinder and the axis line produces a right angle to its base. If one of the circular bases is dismissed it turns into an indirect cylinder.
Radius, height, axis, base, and side are the exact characteristics required to calculate the cylinder. The radius of the cylinder is the radius of the round base. The height is the perpendicular distance among the bases and the line that joins the center from the base is the axis.
Also Read
| Concepts Related to Area of Geometric Figures | ||
|---|---|---|
| Circumference of a Circle | Sphere | Areas Related to Circle |
| Formula of Perimeter Shapes | Diameter Formula | Surface Areas and Volume |
Area of a Cylinder
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The vicinity of a cylinder depends on the curved surface area and the base area.
Curved Surface Area
The curved surface vicinity is the curved surface vicinity of a cylinder with radius ‘r’ and height ‘h’. It can also be called a lateral surface vicinity The formula for a curved area is
Lateral Surface Area= 2*3.14*r*h
Base area
The base area of the cylinder will be circular in shape. Hence,
Area of the circular bases of a cylinder =2 (πr2) [Since the cylinder has two circular bases]
Now the total surface area is no longer a difficult mission.
The total surface area
The total surface area will be the sum of the area of all the faces. It is the curved surface vicinity and the circular vicinity of the cylinder.
Total Surface Area = 2π × r × h + 2πr2= 2πr (h + r) Square units
THE TOTAL SURFACE AREA
Read More: Three-Dimensional Geometry
Derivation
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The region is the shape occupied by it. A cylinder has two circles which can be circles and the curved forms which turn out to be a rectangle. Evaluate the cylinder whose height is 'h' and a circular base with radius, 'r'. Imagine a cylinder and evaluate.
So, the vicinity of the cylinder is the area of the two circles whose base radius is 'r' and the area of the rectangle which is the curved surface.
DERIVATION
Now the vicinity of the cylinder is in the vicinity of two circles whose radius is r and the area of the rectangle (the curved surface). The high point of this rectangle is the high point of the cylinder h, while the length of this rectangle is the circumference of the circle, that is, 2πr. Therefore, the vicinity of this rectangle is the curved surface vicinity of the cylinder, = 2πrh.
Also, total surface area of the cylinder = 2πr2+2πrh = 2πr(h+r)
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Things to Remember
- Total surface area (TSA) of a cylinder of base radius r and height h = 2π × r × h + area of two circular bases
⇒ TSA = 2π × r × h + 2 × πr2
⇒ TSA = 2πr(h + r) (CSA) of a cylinder of base radius r and height h = 2π × r × h - Curved surface area (CSA) of a cylinder of base radius r and height h = 2π × r × h
Sample Questions
Ques: Samuel has given a cylinder of surface area 1728π rectangular devices. Locate the height of the cylinder if the radius of the base of the circle is 24 units? (3 Marks)
Ans: Given that the cylinder has a surface area of 1728π
The area of the base can be used in the following ways, A= 2πr(r + h)
1728π = 2π×24×(h+24)
⇒ 1728/48 = (h+24)
⇒ 36 = h + 24
⇒ h = 12
So, the high point of the cylinder is 12 units.
Ques: The diameter of the bottom of a cylinder is 12 cm and the height is 8 cm. Discover the floor and vicinity of the strong cylinder? (2 Marks)
Ans: Radius = 6 cm
Surface area = 2πr (r + h)
=
= 528 cm2
Ques: A portion of a metal pipe is seen in the diagram below. Given that the internal radius of the pipe is 2 cm, the external ambit is 2.4 cm and the lengthwise pipe is 10 cm. Locate the total surface vicinity of the pipe? (3 Marks)
Ans: r = 2, R = 2.4, h = 10
Total surface vicinity of pipe
= vicinity of internal surface + vicinity of external surface + vicinity of the two rings
= 2πrh + 2πRh + 2(πR2– πr2)
= (2π × 2 × 10) + (2π × 2.4 × 10) + (2 × (2.42π – 22π))
= 40π + 48π + 3.52π
= 91.52π
= 91.52 × 3.142
= 287.56 cm2
Ques: Locate the total surface location of a container in a cylindrical shape whose diameter is 28 cm and height is 15 cm? (3 Marks)
Ans: Given, diameter = 28 cm, so radius = 28/2 = 14 cm
and height = 15 cm
By the formula of total surface are, we understand;
The total Surface Area = 2πr (h + r) = 2x 22/7 x 14 x (15 + 14)
Total Surface Area = 2 x 22 x 2 x 29
Curved surface area(CSA) of a cylinder of base radius r and height h = 2π × r × h
Total Surface Area = 2552 sq.cm
Hence, the total surface vicinity of the container is 2552 sq. cm
Ques: Locate the lateral surface vicinity of a cylinder with a base radius of 3 inches and a height of 9 inches? (3 Marks)
Ans: Lateral surface area=2π(3)(9)=54π square inches
Lateral Surface Area.=2π(3)(9)=54π square inches
≈169.64 square inches
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