surface area of a cylinder

An Introduction to Surface Area of Cylinder

Surface area is the amount of space covering the outside of a three-dimensional shape.

A Cylinder is a 3D structure having round or circular bases parallel to each other. A cylinder has no vertices. Surface area of a cylinder refers to the area occupied by its surface in a three-dimensional space.

The Surface Area of Cylinder = Curved Surface + Area of Circular bases

Formula of Surface Area of a Cylinder

Formula used to calculate the ‘Surface Area of a Cylinder’ is –

Surface area of a cylinder = 2 πr (h+r) sq. unit.

Here π = 3.142 or 22/7, r = radius of the cylinder and h = height of the cylinder.

Example of Surface Area of Cylinder

Now as you have an idea on how to calculate the surface area of a cylinder, let’s have a glance at the examples -

Example 1:

Find the Curved surface area of a cylinder of radius 7 cm and height 14 cm.

Solution: The curved surface area of a cylinder can be calculated using the formula, CSA = 2πrh. After substituting the value of r = 7, h = 14, we get: CSA = 2πrh = 2 × 3.14 × 7 × 14 = 615.8 cm²

Example 2:

What will be the surface of the cylinder with height 10 cm and the diameter of the base is 12 cm.

Solution:

Given, Height = 10 cm Diameter = 12 cm

Hence, Radius = d/2 = 12/2 = 6 cm

According to the formula:

TSA = 2πr(r+h)

2×3.14×6(6+10)

=602.88cm²

Now let us see how to calculate the height of a cylinder if the TSA is given.

Example 3:

Find the height of a cylinder if its total surface area is 2552 in² and the radius is 14 in.

Solution

Given:

TSA = 2552 in²

Radius, r = 14 in.

But, TSA = 2πr (h + r)

2552 = 2 x 3.14 x 14 (14 + h)

2552 = 87.92(14 + h)

Divide both sides by 87.92 to get,

29.026 = 14 + h

Subtract by 14 on both sides.

h = 15

Hence, the height of the cylinder is 15 in.

Curved Surface Area of Cylinder

The curved surface area is defined as the area of only curved surface, leaving the circular top and base.

Consider a cylinder having a height ‘h’ and base radius ‘r’.

The curved surface area of a cylinder is given as-

C.S.A. =2πrh

Example- Consider a curved surface area of a cylinder having height of 5 cm and diameter of base to be 2 cm.

Solution- Given h = 5 cm, and d = 2 cm,

Therefore, r = 1 cm

C.S.A. = 2πrh=2π*1*5=10π

Derivation of Surface Area of Cylinder

By the formula of area of the circle, we know,

Area of the circular base of cylinder = πr²

Since there are two circular bases, the area of both the circular bases = πr² + πr² = 2πr²……….. (1)

Now, from the figure, you can see that the curved surface of the cylinder in two-dimension space forms a rectangle when opened. Hence, the height and circumference of the circular bases are the dimensions of the rectangle formed from it. Therefore,

Area of the curved surface = Height × Circumference

Curved Surface area = h × πd = h × 2πr (since d = 2r)

CSA = 2πrh …………….(2)

By adding equation 1 and equation 2, we get the total surface area, such that;

Total Surface area = Curved Surface area + Area of Circular bases

TSA = 2πrh + 2πr²

By taking 2πr as a common factor from RHS, we get;

TSA = 2πr (h + r)

Therefore, Surface area of a cylinder = curved surface + area of circular bases

In terms of π,

Surface area of a cylinder = 2 πr (h+r) sq unit.

Most Popular Questions Searched By Students:

Q1.How do you find the surface area of cylinder

The sum of the areas of the two circles and the rectangle is:

A= πr²+ πr²+2πrh

By combining like-terms, we can simplify this equation to:

A=2πr(r+h)

Here, A is equal to area, pi is equal to 3.14, r is equal to the radius, and h is equal to the height

Q2.What is the surface area formula?

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape.

Surface Area Formulas: