Area of a Cylinder
In this section, we will learn cylinder definition, formula derivation, and area of cylinder formula along with examples in detail.
Cylinder
A cylinder is a three-dimensional solid shape. It has two parallel faces that have congruent circles. It has a curved surface. The perpendicular distance between the two bases is the height of the cylinder.
Area of Cylinder formula
OR
Where:
Ï€ is a constant whose value is 3.14.
r is the radius.
h is the height of the cylinder
Types of Cylinder
There are two types of cylinder:
- Right Cylinder: If the bases of the cylinder are at the exact position and the axis is at a right angle to the base is called the right cylinder.
- Oblique Cylinder: If the bases of the cylinder are not at the position and the axis is not a right angle to the base, it is called an oblique cylinder.
Derivation
A cylinder is made up of two circles and a rectangle. If you want to derive the formula of area of the cylinder, follow the steps given below:
- Divide the cylinder into three parts: two circles and a rectangle.
- Unroll the sides that form a rectangle.
Calculate the area of each circle separately. We know that the area of the circle is πr2. Adding the area of both circles we get (πr2 + πr2 = 2πr2).
Calculate the area of the rectangle that is width times height. Where h is height, and the length of the cylinder is the distance around the circle. It means it is the circumference of the circle that is 2Ï€r. Hence the area of the rectangle will be 2Ï€r*h.
Now add the area of the circle that is 2Ï€r2 and the area of a rectangle that is 2Ï€rh.
Area of cylinder (A) = 2Ï€r2 + 2Ï€rh
OR
Area of cylinder (A) = 2Ï€r (r + h)
Where:
Ï€ is a constant
r is the radius
h is the height of the cylinder
Examples
Example 1: If the diameter of a cylinder is 15 cm and the height is 7 cm. Find the surface area of the cylinder.
Solution:
We have given, diameter (d) = 15 cm
height (h) =7 cm
we know that, radius is half of the diameter.
r = d/2
r = 15 / 2 = 7.5 cm
We know that,
Area of cylinder (A) = 2Ï€r (r + h)
A = 2 * 3.14 * 7.5 (7.5 + 7)
A = 682.95 cm2
The area of the cylinder is 682.95 cm2.
Surface area of the hollow cylinder
Example 2: The following figure shows a pipe. The internal and external radius of the pipe is 4 cm and 4.4 cm, respectively. The pipe is 9 cm is long. Find the total surface area of the pipe.
Solution:
In this question, we have given two radiuses, internal and external. The r represents the internal radius, and R represents the external radius.
We have given,
r = 4 cm, R = 4.4 cm and h = 9 cm
Total surface area of the pipe (A) = area of internal circle + area of external circle + area of two circles
A=2πrh+ 2πRh+2(πR2– πr2)
A = 2Ï€.4.9 + 2Ï€.(4.4).9 + (2. (Ï€.(4.42)-Ï€.42))
A = 72π + 79.2π +(2. (19.36π – 16π))
A = 72Ï€ + 79.2Ï€ +(2. (3.36Ï€))
A = 72Ï€ + 79.2Ï€ + 6.72Ï€
A = 157.92Ï€
A = 157.92 * 3.14
A = 495.86 cm2
The area of cylinder is 495.86 cm2.