li UNITS OF LENGTH, AREA AND VOLUME 31 



The volume of any rectangular block, or of a cylinder, can be 

 calculated by the application of the same rule. This can be 

 easily understood by referring to the accompanying diagrams 

 (Fig. 19). The base of each block illustrated is divided into 

 units of area say, square centimetres. If we consider the cube 

 to be divided into slices one centimetre thick, each slice could be 

 divided into cubic centimetres, and the number of cubic centi- 

 metres would be the same as the number of square centimetres 

 in the base. Hence, if the base had an area of 30 square centi- 

 metres, the slab 1 centimetre high would contain 30 cubic 

 centimetres. Two such slabs would therefore contain 60 cubic 

 centimetres, three slabs 90 cubic centimetres, and so on for any 

 number of slabs. The volume of any block having the same 

 width and breadth all the way up may evidently be reasoned 



FIG. 19. Volumes of Regular Solids. 



out in the same manner, being equal to the area of the base 

 multiplied by the vertical height. 



To determine the volume of an irregular solid, we proceed by 

 an indirect method as follows : 



EXPT. 42. Fill the cubic inch box with water and pour the 

 water into a narrow glass jar or bottle. Make a mark upon 

 the bottle level with the top of the water. Repeat the opera- 

 tion until the vessel is full of water. A bottle graduated into 

 cubic inches is thus obtained, and it can be used to deter- 

 mine roughly the volume of an irregular solid such as a piece of 

 lead, a glass stopper, a few nails, or any solid heavier than 

 water which will go into the bottle. Fill the bottle about 

 three-quarters full of water, observe the level of the water, 

 and then gently drop in the chosen object. From the rise of 

 water-level which immediately takes place, the volume of the 

 object can be estimated. 



EXPT. 43. Repeat the last experiment, substituting the 



