Centroid of volume is the point at which the total volume of a body is assumed to be concentrated. The volume is having three dimensions i.e., length, width and thickness. Hence volume is measured in [length]3. The centroid [i.e. or centre of gravity] of a volume is obtained by dividing the given volume into a large number of small volumes as shown in Fig. 4.15. Similar method was used for finding the centroid of an area in which case the given area was divided into large number of small areas. The centroid of the volume is hence obtained by replacing dA by dv in equations (4.2 A) and (4.2 B).
Note. If a body has a plane of symmetry, the centre of gravity lies in that plane. If it has two planes of symmetry, the line of intersection of the two planes gives the centre of gravity. If it has three planes of symmetry, the point of intersection of the three planes gives the position of centre of gravity.
Problem 4.12. A right circular cone of radius R at the base and of height h is placed as shown in Fig. 4.16. Find the location of the centroid of the volume of the cone.