A cylindrical shell is a three-dimensional, hollow shape that is formed by rotating a rectangle about an axis parallel to one of its sides.
The formula for calculating the volume of a cylindrical shell is V = 2πrh, where r is the radius of the circular cross-section and h is the height of the shell.
The cross-section volume concept refers to the idea that the volume of a three-dimensional shape can be calculated by finding the area of its cross-section and multiplying it by the length of the shape. This concept is particularly useful for calculating the volume of irregular or non-prism shapes.
The cross-sectional area of a cylindrical shell can be found by using the formula A = πr², where r is the radius of the circular cross-section. This formula can also be used to find the area of a circle.
Cylindrical shells and the concept of cross-sectional volume are used in various fields such as engineering, architecture, and manufacturing. For example, they are used in the design and construction of pipes, tanks, and columns. They are also used in the production of cylindrical objects such as cans and bottles.