Cylinder definition: Solids like circular pillars, circular pipes, circular pencils, measuring jars, road rollers and gas cylinders, etc., are said to be in cylindrical shapes. A cylinder is a solid geometric figure with straight parallel sides and circular top and bottom. This is how we define cylinder.
Cylinder shape: A cylinder is made of two straight sides which are parallel connected by a curved surface.
Formulae:
Let us consider a cylinder whose height is h units and the radius of whose base is ‘r’ units. Then we have:
1. Volume of the cylinder: Volume of a cylinder is the total space included inside the cylinder. Volume of a cylinder is given by the formula = (pi.r^2.h) cubic units.
2. Curved surface area of the cylinder: The curved surface area of a cylinder is given by the formula: (2.pi.r.h) sq. units.
3. Total surface area of cylinder: The total surface area of a cylinder is given by the formula: (area of curved surface) + 2(base area).
= (2.pi.r.h) + (2.pi.r^2) = (2.pi.r.h + 2.pi.r^2) sq. units
Consider a cylinder of radius 10 cm and height 16 cm. The volume of the cylinder will be (pi.r^2.h) cubic units which is equal to [pi. (10)^2.16] which gives 5024 cm^3 and the curved surface area will be (2.pi.r.h) sq. units that is equal to (2. Pi. 10.16) which equals 1004.8 cm^2. The total surface area will be (area of curved surface) + 2(base area) that is (2.pi.r.h) + (2.pi.r^2) = (2.pi.r.h + 2.pi.r^2) sq. units which equals (2.pi.10.16 + 2.pi.10^2) = (1004.8 + 628) = 1632.8 cm^2.
Hollow cylinders: Solid likes iron pipes, rubber tubes, etc., are in the shape of hollow cylinders.
Formulae:
For a hollow cylinder with external radius R units, internal radius r units and height (or length) h units, we have:
1. Volume of material: Volume of a hollow cylinder is the total space included inside the cylinder. Volume of a hollow cylinder is given by the formula = (exterior volume) – (internal volume)
= (pi.R^2.h – pi.r^2.h) cubic units
2. Curved surface area: The curved surface area of a hollow cylinder is given by the formula:
(External surface) + (Internal surface)
= (2.pi.R.h + 2.pi.r.h) sq. units
3. Total surface area: The total surface area of a hollow cylinder is given by the formula:
(Curved surface) + 2(Area of base ring)
= [(2.pi.R.h + 2.pi.r.h) + 2(pi.R^2 – pi.r^2)] sq units
Cylinder shape: A cylinder is made of two straight sides which are parallel connected by a curved surface.
Formulae:
Let us consider a cylinder whose height is h units and the radius of whose base is ‘r’ units. Then we have:
1. Volume of the cylinder: Volume of a cylinder is the total space included inside the cylinder. Volume of a cylinder is given by the formula = (pi.r^2.h) cubic units.
2. Curved surface area of the cylinder: The curved surface area of a cylinder is given by the formula: (2.pi.r.h) sq. units.
3. Total surface area of cylinder: The total surface area of a cylinder is given by the formula: (area of curved surface) + 2(base area).
= (2.pi.r.h) + (2.pi.r^2) = (2.pi.r.h + 2.pi.r^2) sq. units
Consider a cylinder of radius 10 cm and height 16 cm. The volume of the cylinder will be (pi.r^2.h) cubic units which is equal to [pi. (10)^2.16] which gives 5024 cm^3 and the curved surface area will be (2.pi.r.h) sq. units that is equal to (2. Pi. 10.16) which equals 1004.8 cm^2. The total surface area will be (area of curved surface) + 2(base area) that is (2.pi.r.h) + (2.pi.r^2) = (2.pi.r.h + 2.pi.r^2) sq. units which equals (2.pi.10.16 + 2.pi.10^2) = (1004.8 + 628) = 1632.8 cm^2.
Hollow cylinders: Solid likes iron pipes, rubber tubes, etc., are in the shape of hollow cylinders.
Formulae:
For a hollow cylinder with external radius R units, internal radius r units and height (or length) h units, we have:
1. Volume of material: Volume of a hollow cylinder is the total space included inside the cylinder. Volume of a hollow cylinder is given by the formula = (exterior volume) – (internal volume)
= (pi.R^2.h – pi.r^2.h) cubic units
2. Curved surface area: The curved surface area of a hollow cylinder is given by the formula:
(External surface) + (Internal surface)
= (2.pi.R.h + 2.pi.r.h) sq. units
3. Total surface area: The total surface area of a hollow cylinder is given by the formula:
(Curved surface) + 2(Area of base ring)
= [(2.pi.R.h + 2.pi.r.h) + 2(pi.R^2 – pi.r^2)] sq units
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