THE PRISMOIDAL RULE 



253 



height h, the sides of the base being a and b. Let H be the height 

 of the imaginary vertex, and let k and I be the sides of the 

 rectangular section at a distance x from the base. 



f 



Then 



also 



k H - x 



I H - x 



= H< H 

 b 



Thus the area of section = kl. 



FIG. 79. 



If the curve connecting x and A is drawn between the limits 



= and x = h (Fig. 79), the area under this curve will give the 



volume of the frustum, but the curve is a parabola, and as 



