👉 Volumes, a fundamental concept in mathematics, particularly in geometry and calculus, measure the three-dimensional space occupied by a solid object. It is defined as the amount of space enclosed within a boundary, typically calculated using formulas that involve the object's dimensions—length, width, and height (or more generally, for irregular shapes, using integrals). The volume of a simple geometric shape like a cube is straightforward, being the product of its side lengths (V = s³), while for a cylinder, it's πr²h (V = πr²h). For more complex solids, like spheres or cones, specific formulas are used, such as V = (4/3)πr³ for a sphere or V = (1/3)πrh² for a cone. These volumes are crucial in various fields, from engineering and architecture to physics and economics, helping us understand and quantify the space occupied by objects in three dimensions.
