Relation between cylinder and cone volume
Answers
Answer:
he area of its base is indicated in color. ... Therefore, the volume V cyl is given by the equation: V cyl πr 2h (area of its circular base times its height) where r is the radius of the cylinder and h is its height. The volume of the cone (V cone) is one-third that of a cylinder that has the same base and height:
Step-by-step explanation:
Step-by-step explanation:
The volume relationship between these cones and cylinders with equal bases and heights can be expressed mathematically. The volume of an object is the amount of space enclosed within it. For example, the volume of a cube is the area of one side times its height. The figure below shows a cube. The area of its base is indicated in color. Multiplying this (colored) area by the height L of the cube gives its volume. And since each dimension (length, width and height) of a cube is identical, its volume is L × L × L, or L 3, where L is the length of each side.
The same procedure can be applied to finding the volume of a cylinder. That is, the area of the base of the cylinder times the height of the cylinder gives its volume. The bases of the cylinder and cone shown previously are circles. The area of a circle is πr 2, where r is the radius of the circle. Therefore, the volume V cyl is given by the equation: V cyl πr 2h (area of its circular base times its height) where r is the radius of the cylinder and h is its height. The volume of the cone (V cone) is one-third that of a cylinder that has the same base and height: .
The cones and cylinders shown previously are right circular cones and right circular cylinders, which means that the central axis of each is perpendicular to the base. There are other types of cylinders and cones, and the proportions and equations that have been developed above also apply to these other types of cylinders and cones.