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- All three are magnitudes, representing the “size” of an object. Length is the size of a line segment (see distance formulas), area is the size of a closed region in a plane, and volume is the size of a solid. Formulas for area and volume are based on lengths.
www.britannica.com/science/length-area-and-volumeLength, area, and volume | measurement, calculation, shapes ...
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Jul 30, 2024 · Calculate the volume of numerous regular shapes with ease using our versatile volume calculator. Need to calculate the volume of a box? Try this tool.
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The Length to Volume Calculator is a tool used to calculate the volume based on the given length and surface area values. This calculator is particularly useful when working with objects or shapes that have a constant cross-sectional area along their length.
Aug 27, 2023 · Compute the volume of the cube if the side length is (i) \(4.9\) cm and (ii) \(5.1\) cm to compare the estimated uncertainty with the actual potential uncertainty. Solution. a. The measurement of the side length is accurate to within \(±0.1\) cm. Therefore, \(−0.1≤dx≤0.1.\) The volume of a cube is given by \(V=x^3\), which leads to \(dV ...
In dimensional analysis, volume is described as a derived physical quantity from lengths, so its dimension is represented as: [V] = [L3] [V] = [L 3] Here, L L stands for the dimension of length. This notation shows that volume is the product of three lengths. For instance, when calculating the volume of a rectangular prism, you multiply its ...
- Sphere
- Cone
- Cube
- Cylinder
- Rectangular Tank
- Capsule
- Spherical Cap
- Conical Frustum
- Ellipsoid
- Square Pyramid
A sphere is the three-dimensional counterpart of a two-dimensional circle. It is a perfectly round geometrical object that, mathematically, is the set of points that are equidistant from a given point at its center, where the distance between the center and any point on the sphere is the radius r. Likely the most commonly known spherical object is ...
A cone is a three-dimensional shape that tapers smoothly from its typically circular base to a common point called the apex (or vertex). Mathematically, a cone is formed similarly to a circle, by a set of line segments connected to a common center point, except that the center point is not included in the plane that contains the circle (or some oth...
A cube is the three-dimensional analog of a square, and is an object bounded by six square faces, three of which meet at each of its vertices, and all of which are perpendicular to their respective adjacent faces. The cube is a special case of many classifications of shapes in geometry, including being a square parallelepiped, an equilateral cuboid...
A cylinder in its simplest form is defined as the surface formed by points at a fixed distance from a given straight line axis. In common use, however, "cylinder" refers to a right circular cylinder, where the bases of the cylinder are circles connected through their centers by an axis perpendicular to the planes of its bases, with given height h a...
A rectangular tank is a generalized form of a cube, where the sides can have varying lengths. It is bounded by six faces, three of which meet at its vertices, and all of which are perpendicular to their respective adjacent faces. The equation for calculating the volume of a rectangle is shown below: volume= length × width × height EX: Darby likes c...
A capsule is a three-dimensional geometric shape comprised of a cylinder and two hemispherical ends, where a hemisphere is half a sphere. It follows that the volume of a capsule can be calculated by combining the volume equations for a sphere and a right circular cylinder: where r is the radius and his the height of the cylindrical portion EX: Give...
A spherical cap is a portion of a sphere that is separated from the rest of the sphere by a plane. If the plane passes through the center of the sphere, the spherical cap is referred to as a hemisphere. Other distinctions exist, including a spherical segment, where a sphere is segmented with two parallel planes and two different radii where the pla...
A conical frustum is the portion of a solid that remains when a cone is cut by two parallel planes. This calculator calculates the volume for a right circular cone specifically. Typical conical frustums found in everyday life include lampshades, buckets, and some drinking glasses. The volume of a right conical frustum is calculated using the follow...
An ellipsoid is the three-dimensional counterpart of an ellipse, and is a surface that can be described as the deformation of a sphere through scaling of directional elements. The center of an ellipsoid is the point at which three pairwise perpendicular axes of symmetry intersect, and the line segments delimiting these axes of symmetry are called t...
A pyramid in geometry is a three-dimensional solid formed by connecting a polygonal base to a point called its apex, where a polygon is a shape in a plane bounded by a finite number of straight line segments. There are many possible polygonal bases for a pyramid, but a square pyramid is a pyramid in which the base is a square. Another distinction i...
Like units, dimensions obey the rules of algebra. Thus, area is the product of two lengths and so has dimension L 2, or length squared. Similarly, volume is the product of three lengths and has dimension L 3, or length cubed. Speed has dimension length over time, L/T or LT –1.
Length is the size of a line segment (see distance formulas), area is the size of a closed region in a plane, and volume is the size of a solid. Formulas for area and volume are based on lengths.
