Cylinder is one of the basic shapes we have learned in Mathematics. It is a three-dimensional figure having surface area and volume. Here we will learn about its definition, formulas, properties of cylinder and will solve some examples based on them. Apart from this figure, we have concepts of Sphere, Cone, Cuboid, Cube, etc. which we learn in Solid Geometry.
Definition of Cylinder
A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape and the center of the two bases are joined by a line segment, which is called as the axis. The perpendicular distance between the bases is the height, “h” and the distance from the axis to the outer surface is the radius “r” of the cylinder.
Cylinder Formulas-Surface Area and Volume
The cylinder has three major quantities, based on which we have the formulas.
- Lateral Surface Area
- Total Surface Area
Let us see, their formulas now,
- Lateral Surface Area = 2πrh square units
- Total surface area, A = 2πr(r+h) square units
- Volume of the Cylinder, V = πr2h cubic units.
Where ‘h’ is the height and ‘r’ is the radius.
Properties of Cylinder
The basic properties of the cylinder are;
- The bases are always congruent and parallel.
- If axis forms a right angle with the bases, which are exactly over each other, then it is called as “Right Cylinder”.
- It is similar to the prism since it has the same cross section everywhere.
- If the bases are not exactly over each other but sideways, and the axis does not produce the right angle to the bases, then it is called “Oblique Cylinder”.
- If the bases are circular in shape, then it is called a right circular cylinder.
- If the bases are in an elliptical shape, then it is called an “Elliptical Cylinder”.
Question: Find the total surface area of the cylinder, whose radius is 5cm and height is 10cm?
Solution: We know, from the formula,
Total surface area of a cylinder, A = 2πr(r+h) square units
Therefore, A = 2π × 5(5 + 10) = 2π × 5(15) = 2π × 75 = 471.24 cm2
Question: What is the volume of a cylindrical shape water container, whose has the height of 7cm and diameter of 10cm?
Diameter of the container = 10cm
Thus, the radius of the container = 10/2 = 5cm
Height of the container = 7cm
As we know, from the formula,
Volume of a cylinder = πr2h cubic units.
Therefore, volume of the given container, V = π × 52 × 7
V = π × 25 × 7 = 549.778