As with a circle, the longest line segment that connects two points of a sphere through its center is called the diameter, d. Regardless of this distinction, a ball and a sphere share the same radius, center, and diameter, and the calculation of their volumes is the same. Within mathematics, there is a distinction between a ball and a sphere, where a ball comprises the space bounded by a sphere. Likely the most commonly known spherical object is a perfectly round ball. 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. SphereĪ sphere is the three-dimensional counterpart of a two-dimensional circle. This calculator computes volumes for some of the most common simple shapes. Alternatively, if the density of a substance is known, and is uniform, the volume can be calculated using its weight. Beyond this, shapes that cannot be described by known equations can be estimated using mathematical methods, such as the finite element method. The volumes of other even more complicated shapes can be calculated using integral calculus if a formula exists for the shape's boundary. In some cases, more complicated shapes can be broken down into simpler aggregate shapes, and the sum of their volumes is used to determine total volume. Volumes of many shapes can be calculated by using well-defined formulas. By convention, the volume of a container is typically its capacity, and how much fluid it is able to hold, rather than the amount of space that the actual container displaces. The SI unit for volume is the cubic meter, or m 3. Volume is the quantification of the three-dimensional space a substance occupies. Related Surface Area Calculator | Area Calculator Tube Volume Calculator Outer Diameter (d1) Square Pyramid Volume Calculator Base Edge (a) Base Radius (r)Ĭonical Frustum Volume Calculator Top Radius (r) Please provide any two values below to calculate. Rectangular Tank Volume Calculator Length (l)Ĭapsule Volume Calculator Base Radius (r) Sphere Volume Calculator Radius (r)Ĭylinder Volume Calculator Base Radius (r) Please fill in the corresponding fields and click the "Calculate" button. The following is a list of volume calculators for several common shapes. All the other cases can be calculated with our triangular prism calculator.Home / math / volume calculator Volume Calculator The only case when we can't calculate triangular prism area is when the area of the triangular base and the length of the prism are given (do you know why? Think about it for a moment). Using law of sines, we can find the two sides of the triangular base:Īrea = (length * (a + a * (sin(angle1) / sin(angle1+angle2)) + a * (sin(angle2) / sin(angle1+angle2)))) + a * ((a * sin(angle1)) / sin(angle1 + angle2)) * sin(angle2) Triangular base: given two angles and a side between them (ASA) Using law of cosines, we can find the third triangle side:Īrea = length * (a + b + √( b² + a² - (2 * b * a * cos(angle)))) + a * b * sin(angle) Triangular base: given two sides and the angle between them (SAS) However, we don't always have the three sides given. area = length * (a + b + c) + (2 * base_area) = length * base_perimeter + (2 * base_area). If you want to calculate the surface area of the solid, the most well-known formula is the one given three sides of the triangular base : You can calculate that using trigonometry: Length * Triangular base area given two angles and a side between them (ASA) You can calculate the area of a triangle easily from trigonometry: Length * Triangular base area given two sides and the angle between them (SAS) If you know the lengths of all sides, use the Heron's formula to find the area of the triangular base: Length * Triangular base area given three sides (SSS) It's this well-known formula mentioned before: Length * Triangular base area given the altitude of the triangle and the side upon which it is dropped Our triangular prism calculator has all of them implemented. A general formula is volume = length * base_area the one parameter you always need to have given is the prism length, and there are four ways to calculate the base - triangle area. In the triangular prism calculator, you can easily find out the volume of that solid.
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