What is the mathematical formula for calculating volume?

Volume There are different formulas for measuring volumes of different vessels or containers. For a cuboid the formula is length × width × height. This can be generalized for all volumes by multiplying the surface area of the base with the thickness or height, assuming the height of the object is of a uniform shape (i.e.

A cylinder or rectangular prism) When looking at varying values for length, breadth or height, you must separate the varying parts of the unit whose volume you wish to measure For example: a pool which has a shallow end and a deep end. To obtain the volume of the entire pool, you would have to calculate two volumes (one for the shallow end, with a small height, and one for the deep end, with a large height. ) then add the two answers to obtain complete volume.

Or, you could average the height for the entire pool based on average height as a ratio in terms of length. Using that as a value of height, you could then forgo such issues of varying values Another method of measuring volume, especially with irregularly shaped objects is using "displacement. " Fill a cubic container large enough in which to fit the object to be measured with water, measuring the height of the water line and calculating the volume.

Sink the object under the water and take the water line measurement again The second measurement of volume minus the first measurement gives the volume of the object, assuming that the object is enclosed and non-absorbent Specific Formulas Circle pi × radius 2 Annulus pi × (outer radius 2 inner radius 2 ) Trapezoid (bottom base + top base) ÷ (2 × height) Triangle (base × height) ÷ 2 Cube length × width × height Sphere ( 4 3 ) × pi × radius 3 Cylinder pi × radius 2 × height Cone pi × radius 2 × length ÷ 3 Torus (donut) = 2 × pi 2 × (radius of cross-sectional circle center) 2 × (torus radius (center to circle middle)) Or if you want to measure water 1 gram = 1 milliliter = 1 centimeter 3 As an integral in calculus, the volume is the area of a thin slice integrated in a direction perpendicular to the face of the slice. The area must be expressed as a function of the position of the thin slice Note : length and width is the same as: base × height length × height width × height.

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