Measurement of Area and Volume 31 



Find the area of the square in square inches by the 

 method of measurement and calculation given. Find 

 its area also by the method of counting the squares, 

 and compare the results obtained. 



(Note. Should there be any serious discrepancy 

 between the results obtained by the two methods, 

 the student is advised to test the accuracy of the 

 division of the squared paper used by comparing the 

 lengths of the sides of the large and small squares 

 respectively with 0'5 in. and 0*1 in. as given by a well- 

 made scale of inches divided into tenths. A small 

 error in these lengths will cause, when squared and 

 multiplied by the number of squares within the figure, 

 a very considerable error in the value obtained for 

 the area.) 



EXPERIMENT 9. Find the area in square inches of 

 the circle described in Experiment 8 by counting 

 the squares contained within its boundary. (It will 

 be sufficient to count the squares in one quarter-circle 

 or " quadrant ", and multiply the number thus obtained 

 by 4.) 



Find the ratio between the area of the circle and 

 the area of the square on its radius, by dividing the 

 former by the latter. Repeat the experiment by 

 drawing on another sheet of paper a second circle 

 slightly smaller than the first, finding its area as before, 

 and determining the ratio of the area of this second 

 circle to that of the square on its radius. It will be 

 found that the value of this ratio, if the experiment 

 be carefully done, is approximately 3*14. If the 

 experiment be repeated many times, each time with 

 a circle of different radius, it will be found that the 



area of circle 



ratio r ^ is always close to 3-14. 



area of square on radius 



