How to Find Surface Area of a Cylinder Without Height

Surface Area of Cylinder

The surface area of a cylinder can be defined as the total space covered by the flat surfaces of the bases of the cylinder and the curved surface. The total surface area of the cylinder has two components:

curved surface area
flat surface area (of the two flat faces)

Here in this topic, we will discuss what is the surface area of the cylinder and how to calculate the total surface area and lateral surface area of a cylinder. A cylinder is a 3-D solid object which consists of two circular bases connected with a curved face.

1.	What is the Surface Area of a Cylinder?
2.	Formula of Surface Area of a Cylinder
3.	Derivation of Surface Area of Cylinder
4.	How to Calculate Surface Area of a Cylinder?
5.	FAQs on Surface Area of Cylinder

What is the Surface Area of a Cylinder?

The surface area of a cylinder can be defined as the amount of space covered by a flat surface of the base of the cylinder and the curved surface of the cylinder. The surface area of the cylinder is actually the sum of an area of a circle since the base of the cylinder is a circle and the area of curved surface which is a rectangle of length height of the cylinder and circumference of the base as width. Surface area is expressed as the "number of" square units (square centimeters, square inches, square feet, etc.).

cylinder and its parts

Formula of Surface Area of a Cylinder

The formula of the surface area of the cylinder is used to find the surface area occupied by the bases of the cylinder within its boundary and the curved surface of the cylinder. As a cylinder has a curved surface, thus we can express its curved surface area as well as total surface area. A cylinder has two kinds of surface area:

Total Surface Area
Curved Surface Area

If the radius of the base of the cylinder is "r" and the height of the cylinder is "h", the surface area of a cylinder is given as:

Total Surface Area, T = 2πr(h + r)
Curved Surface Area, S = 2πrh

Curved Surface Area of Cylinder

The curved surface area of a cylinder is the area covered by the curved surface. The formula to calculate the curved surface area of a cylinder is given as,

The curved surface area of cylinder = 2πrh
where,

r = Radius of the base of the cylinder
h = Height of cylinder

Total Surface Area of Cylinder

The total surface area of the cylinder is obtained by adding the area of the two bases and the area of the curved surface area. Thus, the formula for the surface area of the cylinder is given as,
Total surface area of cylinder = 2πr²+2πrh = 2πr(h+r)

where,

r = Base radius of the cylinder
h = Height of cylinder

Derivation of Surface Area of Cylinder

The area of any shape is the space occupied by it. A cylinder has 2 flat surfaces which are usually circles and a curved surface that opens up as a rectangle. Consider the cylinder whose height is 'h' and a circular base with radius, 'r'. Let us open a cylinder and see this.

Surface area of cylinder formula and derivation

So, the area 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.

The height of this rectangle is the height of the cylinder h, while the length of this rectangle is the circumference of the circle, that is, 2πr. Thus, the area of this rectangle is the curved surface area of the cylinder, = 2πrh.

Also, total surface area of the cylinder = 2πr²+2πrh = 2πr(h+r)

How to Calculate Surface Area of a Cylinder?

The surface area of a cylinder is equal to the surface area occupied by the bases of the cylinder within its boundary and the curved surface of the cylinder. By following the steps mentioned below we can find the surface area of a cylinder.

Step 1: Note the base radius, 'r', and height, 'h' of the cylinder. Make sure both have the same units.
Step 2: Understand the need to calculate the curved surface area or the total surface area according to the given situation.
Step 3: Implement the formula for curved surface area 2πrh, or total surface area, 2πr(r+h).
Step 4: The answer is in square units of the unit of the length radius.

Now that we know the formula and method to calculate the surface area of the cylinder, let us now understand how to calculate it with the help of some solved examples.

Examples on Surface Area of Cylinder

Example 1: The radius of a cylinder is 5 in. Find the surface area of the cylinder if the height of the cylinder is 15 in. (Take pi as 3.14)

Solution:

Length of the radius, r = 5 in
Height of the cylinder, h = 15 in

Area of the cylinder is: A = 2πr(h+r)
= 2π × 5 ×(15 + 5)
= 10 × 20π
= 628

Therefore, the surface area of the cylinder is 628 square inches.
Example 2: Samuel has given a cylinder of surface area 1728π square units. Find the height of the cylinder if the radius of the base of the circle is 24 units.

Solution:

The surface area of the cylinder, A = 1728π
Using the area of the base is: A = 2πr(h+r)
1728π = 2π×24×(h+24)
⇒ 1728/48 = (h+24)
⇒ 36 = h + 24
⇒ h = 12

So, the height of the cylinder is 12 units.

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Practice Questions on Surface Area of a Cylinder

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FAQs on Surface Area of Cylinder

What Is the Surface Area of a Cylinder?

The surface area of a cylinder is defined as the total area or region covered by the surface of the shape. The surface area of a cylinder is expressed in square units, like m², in², cm², yd², etc.

How Do You Find the Surface Area of a Cylinder?

The surface area of a cylinder can be found following the steps given below,

Step 1: Note down the base radius, 'r', and height, 'h' of the cylinder. Check that the units of dimensions are the same.
Step 2: Apply the formula to find the surface area of a cylinder given as,
LSA of cylinder = 2πrh
TSA of cylinder = 2πr(h + r)
Step 3: Express the answer with a suitable unit.

What Is the Formula to Calculate the Surface Area of a Cylinder?

The formula to calculate the total surface area of a cylinder is given as, the total surface area of cylinder = 2πr(h + r), while the curved surface area of cylinder formula is, curved/lateral surface area of cylinder = 2πrh, where 'r' is the radius of the base and 'h' is the height of the cylinder.

☛Also Check:

Surface Area Formulas
Measurement Formulas

How Do you Find the Surface Area of an Open Top Cylinder?

The surface area of an open-top cylinder can be calculated by finding the area of the base and curved surface. Thus, the area of a cylinder without a top can be given as, the surface area of an open-top cylinder = πr(2h + r), where 'r' is the base radius and 'h' is the height of the cylinder.

What Is the Formula To Find the Base Area of a Cylinder?

The base of a cylinder is circular shaped. Therefore, the formula to find the base area of a cylinder is given as, πr², where 'r' is the base radius of the cylinder.

How Do You Calculate Surface Area of Cylinder Using Calculator?

Surface area of cylinder can be easily evaluated or determine using the surface area of cylinder calculator. It is the fastest method with which we can evaluate the surface area within few seconds. To use the same we need to input the value of the specific parameters in the calculator screen such as a radius, height of the cylinder. Try Cuemath's online surface area of cylinder calculator and get your answers just by a click. Check out surface area of cylinders worksheets for more practice.

How Do You Find the Curved Surface Area of a Cylinder?

The curved surface area of a cylinder is given using the formula, curved/lateral surface area of cylinder = 2πrh, where 'r' is the base radius and 'h' is the height of the cylinder.

What Will Be the TSA of the Cylinder When Curved Surface Area and Base Circumference Is Given?

The TSA of the cylinder when curved surface area and base circumference is given is as, (curved surface area + base area) = (2πrh + πr²) or 2πr(h+r), where 'r' is the base radius and 'h' is the height of the cylinder.

How to Find Surface Area of a Cylinder Without Height

Source: https://www.cuemath.com/measurement/surface-area-of-cylinder/