Objects with definite shapes have a direct formulae that can be applied to determine their volume, V. The formula for the volume of a sphere is V=4/3πr^3. Pi, or π, is a constant and has a numerical value of about 3.14. This formula requires you to know the numerical value of the radius, r, which is fed into the formula and the volume is determined.
The cylinder and cone method is rather complex. First, only half the marble/sphere is taken into account. This hemisphere is then surrounded by a cylinder whose radius and height are equal to the radius, r, of the hemisphere. The volume of the cylinder is V=πr^3. A right cone (same radius and height with the cylinder) with a circular base is inverted and added to the top of the cylinder with its tip at the center of the hemisphere. The volume of the cone is V=1/3πr^3. The volume of the hemisphere is found by subtracting the volume of the cone from the volume of the cylinder. V=πr^3-1/3πr^3=2/3πr^3. The volume of the marble is twice the volume of the hemisphere: V=2*2/3πr^3=4/3πr^3.
A simple definition of the mass, m, of an object is the amount of matter it contains, measured in kilograms; the density, d, is the amount of mass contained per unit volume of an object and is measured as kilograms per cubic unit. Density is a factor related to the material an object is made of; the formula for the density of an object is d=m/V, where V is the volume of the marble. If the mass and density of the marble are known, the equation can be converted to find the volume; the mass divided by the density gives the volume; V=m/d
Volume displacement is the most common method used to find the volume of a marble. A beaker calibrated for volume is used. Water is added into the beaker and the volume is recorded. The marble is then slipped into the beaker and the new volume is recorded. The volume of the marble is the difference between the initial and final recorded volume of water in the beaker.