Volume Formulas

Volume of an object is the amount of space occupied by the object, which is three dimensional in shape. It is usually measured in terms of cubic units. In other words, volume of any object or container is the capacity of the container to hold the amount of fluid (gas or liquid).The volume of three dimensional mathematical shapes Cube, Cuboid, Cylinder, Prism and Cone etc. can be easily calculated by using arithmetic formulas whereas, to find the volumes of complicated shapes, one can use integral calculus.

For example, the volume of the cylinder can be measured as = πr2h, where r = $\frac{d}{2}$ ;
r = radius of the circular base
d = Diameter of the circular base
h = height of the cylinder


Volume of Cylinder

Some of the formulas to find out volumes of basic shapes are –

Shapes Volume Formula Variables
Rectangular Solid or Cuboid l.w.h l = Length,
w = Width,
h = Height
Cube a3 a = length of edge or side
Cylinder πr2h r = radius of the circular edge,
h = height
Prism B . h B = area of base, (B = side2 or length.breadth)
h = height
Sphere $\frac{4}{3}$πr3 r = radius of sphere
Pyramid $\frac{1}{3}$B.h B = area of base,
h = height of pyramid
Right Circular Cone $\frac{1}{3}$πr2h r = radius of the circular base,
h = height (base to tip)
Square or Rectangular Pyramid $\frac{1}{3}$lwh l = length of base,
w = width of base,
h = height (base to tip)
Ellipsoid $\frac{4}{3}$πabc a, b, c = semi – axes of ellipsoid
Tetrahedron $\frac{\sqrt{2}}{12}$$a^{3}$ a = length of the edge

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Practise This Question

The primary coil of a transformer contains 100 turns; the secondary has 200 turns. The primary coil is connected to a size AA battery that supplies a constant voltage of 1.5 volts. What voltage would be measured across the secondary coil?