Volume and Surface Area

Volume and surface area are fundamental concepts in geometry used to measure physical attributes of three-dimensional shapes.

Volume

The volume of a three-dimensional figure is the number of cubic units that can fit inside it. It is a measure of the space enclosed by the figure. For example, the volume of a cube with side length a is given by a³, while the volume of a rectangular prism with length l, width w, and height h is given by lwh.

Surface Area

The surface area of a three-dimensional figure is the total area of all surfaces that make up the figure. It is the sum of the areas of all faces or curved surfaces of the figure. For example, the surface area of a cube with side length a is given by 6a², while the surface area of a rectangular prism with length l, width w, and height h is given by 2lw + 2lh + 2wh.

Applications

Volume and surface area are used in a wide variety of fields, including engineering, architecture, physics, and everyday life. They are used to calculate the capacity of containers, the space within structures, the amount of material required to cover objects, and much more.