In mathematics, we have two different kinds of figures. Namely - Plane shapes and solid shapes. The solid shapes are three-dimensional. A cylinder is one among them. Several examples were available in our daily life, like gas cylinders, water tanks, cylindrical flasks, etc. Let's see the volume of a cylinder formula with the help of the formula area of the cylinder and the volume of the circle formula.
The formula for the volume of a Cylinder helps to calculate the capacity and space available in it. If we observe the structure of a cylinder, it has a curved surface in the middle and circular faces at ends. First, we need to know the formula area of cylinder and the volume of circle formula. The summation of these two formulae can easily provide the volume of a cylinder formula.
We need to consider the formula area of the cylinder for deriving the volume of cylinder formula.
If two circular surfaces are packed one upon the other with the support of a curved surface in the middle, then it is known as a cylinder. To get the formula for the volume of a cylinder, let's find the volume of each surface separately.
Let us assume that 'h' is the height of a curved surface.
We know that the formula for the area of a circle is πr².
By adding these two, we will get the formula of the cylinder.
The volume of cylinder = πr²h
Where r - radius of the circle.
Hence the product of height with the area of the circle gives the volume of the cylinder. It is also known as the volume of the right circular cylinder.
∴ Volume of a Cylinder = πr²h
Cone and cylinder both have circular faces. So both volumes require an area of a circle formula. Here also, the height 'h' is considered for the Cone.
Representation of the formulae for the volume of Cone and cylinder are -
Volume of a Cylinder = πr²h
The volume of a Cone = ⅓(πr²h)
Hence the volume of circle formula is derived. It helps find the capacity of a container, perfume bottle, cylindrical flasks in chemical labs, water tanks, etc., easily. Also, the space occupied in it becomes simple with this formula.
1. Differentiate Between Cone and Cylinder.
Ans. In mathematics, cones and cylinders both are solid shapes that are three dimensional. Besides, few similarities, both the cone and cylinder have several differences. Considering the similarities, both have a circular surface that has radius and circumference.
Apart from these similarities, let's talk about the differences between both cone and cylinder. A cylinder is a solid figure which is enclosed by two parallel lines between two circular surfaces. The parallel lines can be considered as the height of the cylinder. The extreme positions may not be circular in all cases. On the other hand, corn is a solid figure formed with a circular base joining two non-coplanar line segments. These two line segments will intersect at one point and form the shape of the cone. The cone has two surfaces; one is the base, and the other is the apex. The base surface is a complainer surface, and the Apex surface is non-coplanar. We have two different types of cones, namely - oblique circular cones and right circular cones.
Another major difference between the cone And the cylinder is that the cone is one-third of a cylinder concerning its volume.
2. Define the Area and Volume of a Figure?
Ans. In mathematical terminology, especially in geometry, the area of a solid figure can be defined as the amount of space occupied by the flat surface in a closed figure. It can be measured by dividing the surface into equal squares. That's the reason the measuring units of area are square centimeters, square meters, square feet etc. The calculation of the area is from one solid figure to another.
On the other hand, the volume of a solid figure can be defined as the space occupied by the surface in a three-dimensional view. Also, it is explained as the space occupied within the boundary of an object. It is calculated and expressed in terms of cubic units, namely cubic centimeters, cubic meters, cubic inches, cubic feet etc.
3. What are the Properties of a Cylinder?
Ans. Cylinder is a three-dimensional solid figure which has the following properties.
A cylinder has two edges and three faces.
A cylinder doesn't have any vertices.
Two identical surfaces are available at the extreme positions of a cylinder.
Examples of cylinders are - gas cylinder, batteries, food tins, water containers etc.