MEASUREMENT OF VOLUME 



21 



number of square centimetres in the base. Hence, if the base had 

 an area of 30 square centimetres, a 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 parallel ends, and the same 

 width and breadth all the way up may evidently be reasoned out in 

 the same manner, being equal to the area, of the base multiplied by the 

 vertical height. 



Rule. The volume of a prism or cylinder = area of the base x height. 



Metric Measures of Length and Capacity. 



British and Metric Equivalents. 



1 inch = about 24- centimetres. 

 1 foot = ,, 3 decimetres. 

 1 yard = ,, T 9 7 metre. 

 1 mile = ,, If kilometre. 

 1 gallon = ,, 41 litre. 



1 cm. = about f in. 

 1 dm. = ,, 4 in. 

 1m. = ,, 3 ft. 3 in. 

 1 km. = ,, f mile. 



1 litre = 



If pints. 



QUESTIONS ON CHAPTERS III. AND IV. 



7. A rectangular plot of ground is 100 yards in length and 60 yards in 

 breadth, a walk 4 feet broad going round the ground close to and inside the 

 boundaries of the plot. 



What is the area of the walk ? 



What percentage of the total area is occupied by the walk ? 



8. Using squared paper, prove that the area of any triangle equals the 

 altitude multiplied by half the base. 



9. Prove by the use of squared paper : 



(a) that triangles of different shapes but of equal bases and altitudes are 

 equal in area ; 



(6) that the area of a triangle equals half the product of the lengths 

 of the base and altitude. 



10. A solid circular cylinder the diameter of which is 7 cm. and the height 

 12 cm. is cut into two equal parts by a plane through the axis. 

 Calculate the total surface area and also the volume of one of the parts. 



