Volume is the quantity of three dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains.Volume is often quantified numerically using the cubic meter.
The volume of a container is generally understood to be the capacity of
the container, i. e. the amount of fluid (gas or liquid) that the
container could hold, rather than the amount of space the container
itself displaces.
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
(a is the length of the side of each edge of the cube)
Volume of a Cube = a*a*a
rectangular prism:
(a, b, and c are the lengths of the 3 sides)
Volume of a Rectangular Prism = a*b*c
A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder.
('h' is height of the cylinder and 'r' is the radius of base)
Volume of a Cyinder = pi*r*r*h
prism:
( 'h' height and 'b' base area )
Volume of a prism = b*h
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid with polygonal base. A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges. All pyramids are self-dual.
( 'h' height and 'b' base area )
Volume of a pyramid = 1/3*b*h
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.
( where 'r' radius of the base and 'h' is height)
Volume of a Cone = 1/3*pi*r*r*h
A sphere is a perfectly round geometrical and circular object in three-dimensional space that resembles the shape of a completely round ball. Like a circle, which, in geometric contexts, is in two dimensions, a sphere is defined mathematically as the set of points that are all the same distance r from a given point in three-dimensional space. This distance r is the radius of the sphere, and the given point is the center of the sphere. The maximum straight distance through the sphere passes through the center and is thus twice the radius; it is the diameter.
(r is radius of circle)
Volume of a Sphere = 4/3*pi*r*r*r
Volume of a ellipsoid = (4/3) pi r1 r2 r3
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
Volume of a Cube = a*a*a
rectangular prism:
Volume of a Rectangular Prism = a*b*c
A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder.
Volume of a Cyinder = pi*r*r*h
prism:
Volume of a prism = b*h
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid with polygonal base. A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges. All pyramids are self-dual.
Volume of a pyramid = 1/3*b*h
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.
Volume of a Cone = 1/3*pi*r*r*h
A sphere is a perfectly round geometrical and circular object in three-dimensional space that resembles the shape of a completely round ball. Like a circle, which, in geometric contexts, is in two dimensions, a sphere is defined mathematically as the set of points that are all the same distance r from a given point in three-dimensional space. This distance r is the radius of the sphere, and the given point is the center of the sphere. The maximum straight distance through the sphere passes through the center and is thus twice the radius; it is the diameter.
Volume of a Sphere = 4/3*pi*r*r*r
Volume of a ellipsoid = (4/3) pi r1 r2 r3
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