Surface Area Of A Cylinder Formula

Surface Area Of A Cylinder Formula

The Surface Area Of A Cylinder Formula can be defined as the total space covered by the plane of the cylinder base and its curved surfaces. The total Surface Area Of A Cylinder Formula has two components, a curved region and two planar regions. Learn more about what the surface area of a cylinder is and how to calculate the total and lateral area of a cylinder.

Consider the following diagram showing the different parts of a cylinder used to find the Surface Area Of A Cylinder Formula: Students can see the Surface Area Of A Cylinder Formula and other formulas on the website of Extramarks which provides accurate and authentic information on each topic.

What is the Surface Area of a Cylinder?

What is the surface cylinder? The Surface Area Of A Cylinder Formula can be defined as the amount of space covered by the plane of the base of the cylinder and the curved surface of the cylinder. The total area of ​​a cylinder includes the areas of the two bases of the circular cylinder and the area of the curved surface. Surface Area Of A Cylinder Formula is expressed in square units such as square centimeters, square inches, and square feet. A cylinder is a three-dimensional solid object consisting of two circular bases connected by a curved surface. 

Formula Of Surface Area Of A Cylinder 

The Surface Area Of A Cylinder Formula is used to determine the surface area occupied by the base of the cylinder and the curved surface of the cylinder. Since a cylinder has a curved surface, it can represent curved surfaces as well as fully curved surfaces. This means that a cylinder has two surface areas: the total surface area (TSA) and the curved area (TSA).

Curved Surface Area Of Cylinder

cylindrical surface

A curved surface of a cylinder is a surface covered only by that curved surface. If the radius of the base of the cylinder is ‘r’ and the height of the cylinder is ‘h’, the curved surface of the cylinder is calculated by the formula:

Cylindrical curved surface 

Cylinder surface = 2πrh

Where,

r = radius of the cylinder

h = cylinder height

pi = 22/7 or 3.14

Curved Surface Area Of Cylinder Formula

Example: Find the curved surface of a cylinder with a radius of 7 cm and a height of 14 cm.

Solution: The surface of a cylinder can be calculated using the formula CSA = 2πrh. Substituting values ​​for r = 7 and h = 14, we get: CSA = 2πrh = 2 × 3.14 × 7 × 14 = 615.8 cm2

Total Surface Area of Cylinder

the entire surface of the cylinder

The total area of a cylinder is obtained by adding the areas of the two bases and the area of the curved surface. Therefore, the formula for the total Surface Area Of A Cylinder Formula is:

Total area of ​​cylinder = area of ​​2 bases + area of ​​curved surface. Since the bases of the cylinders are circular, their combined area is πr2 + πr2. We already know that the surface of the cylinder is 2πrh.

Total Surface Area Of Cylinder = 2πr(r+h)

Total area of ​​cylinder ⇒ (πr2 + πr2) + 2πrh

⇒ 2πr2 + 2πrh

Total Surface Area Of A Cylinder Formula = 2πr(r+h)

Where, 

r = radius of the cylinder

h = cylinder height

Example: Find the total surface area (TSA) of a cylinder with a radius of 5 cm and a height of 8 cm. 

Solution: The total surface area (TSA) of a cylinder will be calculated by the formula 

TSA = 2πr(r + h) then substituting the values ​​r = 5 and h = 8, we get TSA = 2πr(r + h) = 2πr(r + h) = 2 × 3.14 × 5(5 + 8) = 615.8 cm2. Must visit Extramarks for Surface Area Of A Cylinder Formula and other formulas.

Derivation Of The Formula For The Surface Area Of Cylinder

Derivation of the formula for the Surface Area Of A Cylinder Formula

An arbitrarily shaped region is the space it occupies. A cylinder has two flat faces that are circles and a curved face that opens out as a rectangle. Consider the following cylinder with height ‘h’ and radius ‘r’. Let’s try to understand this by opening the cylinder in two dimensions. Cylindrical surfaces and derivations

 Notice the diagram above. The curved face opens as a rectangle with two bases that are circles.

Now the two circles have an area of ​​(πr2 + πr2) and a base radius of ‘r’. One side of the rectangle is the height of the cylinder, h, and the length of this rectangle is the circumference of the circle, so 2πr. So the area of ​​this rectangle is (l × b) = 2πr × h = 2πrh, which is also the curved surface of the cylinder. So the total Surface Area Of A Cylinder Formula = 2πr2 + 2πrh = 2πr(r + h)

Extramarks is the best website for the Surface Area Of A Cylinder Formula

How To Calculate The Surface Area Of A Cylinder?

The Surface Area Of A Cylinder Formula is equal to the surface area occupied by the base of the cylinder and the curved surface of the cylinder. Use the following procedure to find the total surface area of ​​a cylinder with a radius of 7 units and a height of 9 units.

Step 1: Students should note the radius “r” and height “h” of the cylinder and make sure that both are in the same units. where r = 7 and h = 9

Step 2: For the given question, we need to find the total surface area of ​​a cylinder, so we use the formula for the total surface area of ​​a cylinder, total Surface Area Of A Cylinder Formula = 2πr(r + h).

Step 3: Substitute the given value and express the result in square units. Substituting the values ​​into the formula gives the total Surface Area Of A Cylinder Formula = 2πr(r + h)

=2π × 7(7 + 9) 

=2π × 112 

=2 × 3.14 × 112 =703.6 square units. 

Examples On Surface Area Of Cylinder

Example 1: If the radius of the cylinder is 5 inches and the height of the cylinder is 15 inches, then calculate the Surface Area Of A Cylinder Formula (assuming a pi value of 3.14)

SOL: 

Radius, r = 5 inches

Cylinder height, h = 15 inches 

 Cylinder surface: A = 2πr(r+h)

= 2π × 5 × (5 + 15)

= 2π × 5 × 20

= 628 

 So the Surface Area Of A Cylinder Formula will be 628 square inches.

 Example 2: Samuel has a cylinder with a surface area of ​​1728 pi square units. Find the height of the cylinder when the base radius of the circle is 24 units. 

Sol: Surface of Cylinder will be A = 1728π ; Radius will be (r) = 24; h = not known then the given values into the formula to find the height of the cylinder.

A = 2πr(r + h)

1728π = 2π × 24 × (24 + h)

⇒ 1728/48 = (24 + hours)

⇒ 36 = (24 + hours)

⇒h=12

Therefore, the cylinder is 12 units tall.

Example 3: Specify true or false.

a.) The total area of ​​a cylinder is obtained by adding the areas of the two bases and the curved surface. b.) The total Surface Area Of A Cylinder Formula is calculated using the formula total surface area = 2πrh.

SOL:  a.) Correct, the total area of ​​a cylinder is obtained from the sum of the areas of the two bases and the area of the curved surface.

b.) Wrong. The total surface area of ​​a cylinder is calculated by: Total Surface Area Of A Cylinder Formula = 2πr(r + h)

 Practice Questions On Surface Area Of A Cylinder

1. What is meant by the surface of a cylinder? 

The surface area of ​​a cylinder is defined as the total area or area covered by the surface of a shape. A cylinder has two flat surfaces and one curved surface, so the total area includes the area of the flat surface and the area of ​​the curved surface. The Surface Area Of A Cylinder Formula is expressed in square units such as m2, in2, cm2, yd2.

 How do you find the surface of a cylinder?

The surface area of ​​a cylinder can be found using the following steps.

Step 1: Note the radius “r” and height “h” of the base of the cylinder. Students should make sure the units of measure are the same. Step 2: Find the Surface Area Of A Cylinder Formula by applying the following Formula:

Cylinder surface = 2πrh

total surface area of ​​cylinder = 2πr(h + r)

Step 3: Then, students must substitute the given values and express the answer in square units. 

 What is the formula for the total surface area of ​​a cylinder?

The formula for calculating the total surface area of ​​a cylinder is expressed as the total surface area of ​​the cylinder = 2πr(r + h). This total surface area includes two basal (2πr2) and curved (2πrh) regions where ‘r’ is the cylinder radius and ‘h’ is the height. 

 How do you find the Surface Area Of A Cylinder Formula of ​​an open-topped cylinder?

 You can calculate the Surface Area Of A Cylinder Formula of ​​an open-topped cylinder by finding the area of ​​the base and the curved surface. Therefore, the area of ​​a cylinder without a top can be expressed as the Surface Area Of A Cylinder Formula with an open top = πr(r + 2h) where ‘r’ is the radius and ‘h’ is the height of the cylinder. Since the cylinder does not have a top, the surface of the base was removed. 

1. What is the curved surface of a cylinder with a radius of 7m and a height of 10m?

The curved surface of a cylinder can be calculated using the following formula: Cylinder surface = 2πrh. where r = cylinder radius and h = cylinder height. Substituting the values ​​of the equation for r = 7 and h = 10, we get: Cylinder surface = 2πrh = 2 × 3.14 × 7 × 10 = 439.6 m sq. For more examples of the Surface Area Of A Cylinder Formula students can visit Extramarks.