Cylinder Volume Cylinder Volume In this session we are going to learn about Cylinder Volume. Volume is a very interesting and important topic of geometry. Volume in general is a quantity of any space in 3 dimensional views which is closed by some boundary; for instance the space that a container or shape occupies or fills. The substance that is to be filled can be solid, gas or liquid. The volume of any container is also known as the capacity of that container for example glass, plate etc are the containers and the volume is their capacity of containing the substance. Now the next question arises is that what the cylinder is. A cylinder is a curvilinear shape in geometry whose surface is made up of the points which resides at a fixed distance from the given segment of the line. This segment of line is called the axis of the cylinder. It is a solid container which is enclosed by the surface and by two planes which are perpendicular to the line segment or the axis is known as the cylinder. A cylinder is a finite section or part of a right circular cylinder. In cylinder the lines are
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perpendicular to the bases and it has a radius and length as its parameters. We use these two parameters for calculating the volume of the cylinder. If radius of the cylinder is R and length or height is H then the volume of the cylinder can be given as: V = πR^2 H And the surface area of the cylinder is given as A =2πR^2 + 2πRH = 2πR(R + H) Here the area of the top of the cylinder is πR^2 and the area of the bottom of the cylinder is πR^2 and the area of its side is given as 2πRH. The cylinder which has the smallest area has Height = 2 * R. The cylinder which has the largest volume has Height = 2 * R and it fits in a cube shape if the Height is equal to the Diameter of the cylinder. Now to understand this let’s take some example. 1.
Find the volume of the cylindrical canister whose radius is 10m and height is 15m.
In the question given the radius R = 10m and height H = 15m then Volume of the cylinder = πR^2 H
(using the formula)
V = (22/7) * (10)^2 * (15)
(put all the values)
V = (22/7) * 100 * 15
(solve it)
V = 22/7 * 1500
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V = 4714.28 m
(Answer)
2. The height of the cylinder is 14 inches and its volume is 144 inches so calculate the radius of the cylinder. Cylinder Volume = πR^2 H
(using the formula)
144 = (22/7) * R^2 * 14 R^2 * 44 = 144 R^2 =144/44 R^2 =3.27 inches So the radius of this cylinder is the root value of 3.27 inches.
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