Area Of a Cylinder

Title:- Area Of a Cylinder

Introduction:-

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A cylinder is a three-dimensional geometric shape which is defined as a solid composed of two congruent circular bases and a curved surface that joins them. The formula used to calculate the surface area of a cylinder is based on the circle, which means that its area is proportional to the size of its base. In this article, we will explore the Area Of a Cylinder in detail.

Explanation:-

What is the Area Of a Cylinder?

Answer:-  The surface area of a cylinder or Area Of a Cylinder can be defined as the total space surrounded by the flat surfaces of the bases of a cylinder and its curved surface. The total surface area of the cylinder has two parts - one curved surface area and two flat surface areas.

Formula for Calculating the Area of a Cylinder:-

The formula used to calculate the surface area of a cylinder or Area Of a Cylinder is given by:
A = 2πr² + 2πrh
Where:
- A represents the surface area of the cylinder.
- r represents the radius of the circular base of the cylinder.
- h represents the height of the cylinder.
The formula can be broken down into two parts. The first part (2πr²) represents the area of the two circular bases, while the second part (2πrh) represents the area of the curved surface that joins the two bases.
To use the formula, first, we will calculate the area of the two circular bases (2πr²) and will add them together. Next, we will calculate the area of the curved surface (2πrh) and we will add it to the total. The sum of the two will give us the surface area of the cylinder.

What is Curved Surface Area of Cylinder?

Answer:- The curved surface area is defined as the area of only curved surface, leaving the circular top and base.
           The formula for a curved area or lateral area can be defined by: CSA or LSA = 2π × r × h Square units.

Example of Calculating Curved Surface Area of a cylinder.

Let, us take an example to illustrate how to calculate the curved surface area (C.S.A) of a cylinder
Example(1):-
A cylinder has a diameter 14 cm and its height is 10 cm, find its curved surface area (C.S.A)
Answer:- Here,
         radius( r)  = 14/2 cm = 7 cm
        height ( h) = 10 cm
 Step (1): Perimeter of its curved surface 
            = 2πr
            = 2 × 22/7 × 7 [ ∵ putting π = 22/7 ]
            = 44 cm
   Step (2) : We will multiply curved surface are by the height of the cylinder.
   ∴ Curved surface area of the cylinder
   (C.S.A) =  2πr × h
                = (44  × 10) cm²
                = 440 cm²

Example of Calculating the Area of a Cylinder:-

Let's take an example to understand how to calculate the area of a cylinder.
Example(2):-
Let, us Consider a cylinder which has a radius of 4 cm and a height of 10 cm.

Answer:- 
1st, Method:-
Step 1: We will Calculate the area of the circular bases
Area of the circular base = πr²
= π(4 cm)²
= 16π cm²
Since there are two circular bases, the total area of the circular bases will be:
2 × (16π cm²) = 32π cm²
Step 2: We will Calculate the area of the curved surface
Area of the curved surface = 2πrh
= 2π(4 cm)(10 cm)
= 80π cm²

Step 3: Now we will add the areas of the circular bases and the curved surface
∴Total area of the cylinder = 32π cm² + 80π cm²
= 112π cm²
Therefore, the surface area of the cylinder with radius 4 cm and height 10 cm is 112π cm².
2nd Method:-
        Here,
                radius (r) = 4 cm
               height (h) = 10 cm
  ∴ Area of the cylinder = 2πr² + 2πrh
                               = 2πr (r+ h)
                              = 2 × π × 4 ( 4 + 10)
                              = 8 π ( 14) cm²
                              = 112π cm²
   Step 1 :  Total base area is added with curved surface area of the cylinder.
 Step 2 : 2πr have been taken common and we have got (r + h) as a factor
 Step 3 : Values of r and h are put
Step 4 : Calculating we have got the area of the cylinder is 112 π cm²

                                

 Application of the Area of a Cylinder:-

The concept of the area of a cylinder has several practical applications. For example, it is used to calculate the volume of a cylinder, which in turn is used in various fields such as engineering, physics, and construction.
The area of a cylinder is also used to calculate the capacity of tanks, pipes, and other cylindrical containers. This information is essential for industries that require the transportation of liquids or gases such as oil and gas, chemical manufacturing, and food and beverage.

Conclusion:-

In conclusion, the surface area of a cylinder or Area Of a Cylinder can be calculated using the formula A = 2πr² + 2πrh. This formula is essential in various fields such as engineering, physics, and construction. Knowing how to calculate the area of a cylinder is useful for solving real-world problems, from calculating the volume of a cylinder to determining the capacity of ..............

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FREQUENTLY ASKED QUESTIONS ON Area Of a Cylinder:-

(i).What is the area of the cylinder?

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Answer:The area of the cylinder or total surface area of cylinder = 2πr(r + h),where r = radius and h = height of the cylinder.

(ii).What is the formula for area of cylindrical tank?

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Answer:The formula for area of cylindrical tank = 2πr² + 2πrh, where r = radius of the cylindrical tank and h = height of the cylindrical tank.

(iii).What is the CSA of a cube?

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Answer:CSA of a cube = 4l², where l = length of each face of the cube.

(iv).What is volume of the cone?

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Answer:The volume of the cone can be given = ⅓ πr²h, where r = radius of the cone and h = height of the cone.

(v).What is the area of hollow cylinder?

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Answer:The area of hollow cylinder can be given = 2π(R + r)h + 2 π (R² - r²) where,

R = External radius of the hollow cylinder

= Internal radius of the hollow cylinder.

and h = height of the hollow cylinder.

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