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PRACTICAL MATHEMATICS 



(5) The following values of x and y give the co-ordinates of a 

 number of points on a curve. Plot the points and draw the curve. 



Take the area bounded by the curve, the ordinates at x = 

 and x = 9, and the axis of x. By dividing this area into 18 vertical 

 strips of equal breadth, find (1) the area, (2) the distance of the 

 centroid from the axis of y, (3) the volume of the surface of re- 

 volution generated as the area rotates about the axis of y, (4) 

 the moment of inertia of the area about the axis of y, 



(6) Divide the area in Question 5 into 12 horizontal strips of 

 equal breadth, and find (1) the area, (2) the height of the centroid 

 above the axis of x, (3) the volume of he surface of revolution 

 generated as the area rotates about the axis of x } (4) the moment 

 of inertia of the area about the axis of x. 



(7) In the figure of Question 5 take P, a point on the axis of x, 

 so that x = 4-5. Use this point to draw the first and second derived 

 figures. Find the areas of these figures and use your results to 

 find (1) the height of the centroid above the axis of x, (2) the 

 moment of inertia of the area about the axis of x. 



(8) In the figure of Question 5 take Q, a point on the axis of y, 

 so that y = 2. Use this point to draw the first and second derived 

 figures. Find the areas of these figures, and use your results to 

 find (1) the distance of the centroid from the axis of y, (2) the 

 moment of inertia of the area about the axis of y. 



(9) The following values of x and y give the co-ordinates of a 

 number of points on a closed curve. Plot the points and draw 

 the figure. 



By dividing the figure into 16 vertical strips of equal breadth, 

 find (1) the area, (2) the distance of the centroid from the axis of 

 y, (3) the volume of the surface of revolution generated as the figure 

 rotates about the axis of y, (4) the moment of inertia about the axis 

 of y. 



(10) By dividing the figure of Question 9 into 12 horizontal strips 

 of equal breadth, find (1) the area, (2) the height of the centroid 

 above the axis of x, (3) the volume of the surface of revolution 

 generated as the figure rotates about the axis of x, (4) the moment 

 of inertia about the axis of x. 



