## Area of a CylinderIn this section, we will learn cylinder definition, formula derivation, and area of cylinder formula along with examples in detail. ## CylinderA 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 formulaArea of cylinder (A) = 2πr^{2} + 2πrhOR Area of cylinder (A) = 2πr (r + h)
π is a constant whose value is 3.14. r is the radius. h is the height of the cylinder ## Types of CylinderThere 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.
## DerivationA 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 (πr.^{2 }+ πr^{2} = 2πr^{2})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 Now add the area of the circle that is 2πrh.
π is a constant r is the radius h is the height of the cylinder ## Examples
We have given, diameter (d) = 15 cm height (h) =7 cm we know that, radius is half of the diameter.
r = 15 / 2 = 7.5 cm We know that,
A = 2 * 3.14 * 7.5 (7.5 + 7) A = 682.95 cm
In this question, we have given two radiuses, internal and external. The 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 = 2π.4.9 + 2π.(4.4).9 + (2. (π.(4.4 A = 72π + 79.2π +(2. (19.36π - 16π)) A = 72π + 79.2π +(2. (3.36π)) A = 72π + 79.2π + 6.72π A = 157.92π A = 157.92 * 3.14 A = 495.86 cm
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