Question

The figure below shows a solid with both rectangular and triangular cross sections. Let a = 9, b = 7, and c = 16.
http://www.webassign.net/hgmcalc/8-1-31fig.gif


(a) Slice the solid parallel to the triangular face. What is the approximate volume of the slice in terms of x, the distance of the slice from one end.

(b) Repeat part (a) for horizontal slices. Instead of x, use h, the distance of a slice from the top.

Answer 1

part (a),
the area of the triangle=(1/2)ac
the volume at a distance x is=(1/2)acx
where a=9, c=16, 0<x<=b=7

Answer 2

what about part "b"?

Answer 3

part (b),



so the area of rectangle cut parallel with horizontal plane at height h is=bc'=b(hc/a)=bch/a

Answer 4

so the volume at height h is=area*(h/2)=(bch/a)(h/2)=(1/2)abc(h/a)^2
where 0<h<=a=9

Answer 5

what about ((c/a)(a-h))b *(delta h)

Answer 6

yes good.
integrate it from 0 to a.