All about a cylinder
A cylinder is an important geometrical shape. If you look around, you can see a lot of objects in the shape of a cylinder.To calculate curved surface area,total surface area and volume of a cylinder is very important in many situations.
Before starting this, we must know about prism.
Prism
Prism is a three dimensional solid. A prism has two equal ends. The ends are called bases. The bases can be circle,triangle,square , rectangle or any other polygon. Faces other than the bases are called lateral faces. The lateral faces are rectangles (except cylinder).
If the number of sides of base of a prism is n , then
Number of faces = n+2
Number of vertices = 2n
Number of edges = 3n
Cylinder
A cylinder is a prism. A cylinder is a closed three dimensional solid that has two parallel bases connected by a curved surface at a fixed distance called height of the cylinder. These bases are normally circular in shape and the center of two bases are joined by a line segment which is called the axis of the cylinder.
h is the height and r is the base radius of a cylinder.
Base area is the area of its base
Base area of a cylinder =𝜋r2
Base perimeter is the perimeter of its base
Base perimeter = 2𝜋r
Lateral surface area or curved surface area is the area of the curved surface of a cylinder contained between the two parallel circular bases.
Lateral surface area is the product of base perimeter and height
Lateral surface area or curved surface area = 2𝜋rh
Total surface area
Total surface area of a cylinder is the sum of curved surface area and the area of two circular bases.
Total surface area = curved surface area + 2 × base area
= 2𝜋rh + 2×𝜋r2
= 2𝜋r(r+h)
Volume
The volume of a cylinder is the space occupied by the cylinder.
Volume is the product of base area and height
Volume = base area×height
= 𝜋r2 × h
= 𝜋r2h
The formula to find curved surface area, total surface area and volume is very helpful in many life situations. So everyone must be aware of these formulas.
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