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A rectangular solid (box) is a prism bounded by six rectangles. The solid can be formed from a pattern of six rectangles, as shown in Fig. 17-3, folded along the dashed lines. The length l, width w, and height h are its dimensions. A cube is a rectangular solid bounded by six squares. The cube can be formed from a pattern of six squares, as shown in Fig. 17-4, folded along the dashed lines. Each equal dimension is represented by e in the diagram.

The first run generates 20 integers uniformly distributed between 1 and 100. The second run generates

Sub Averages(a As Single, b As Single, c As Single, d As Single) c = Sqr(a ^ 2 + b ^ 2) d = Sqr(a * b) End Sub Dim X As Single, Message As String Randomize X = -1 + 2 * Rnd Call SignIs(X, Message) MsgBox(Message)

Fig. 17-4

20 integers uniformly distributed between 22 and 66. In the for loop, we divide rand ( ) by 100 first to strip way the two right-most digits of the ran-

Fig. 17-5

dom number. This is to compensate for the problem that this particular random number generator has of ~ producing numbers that alternate odd and even. Then rand ( ) / 10 0 %range produces random numbers in the range 0 to range-l, and rand ( ) / 10 0 %range + min produces random numbers in the range min to max.

A much better amxoach to generating Dseudo-random numbers is described in Problem 8.20. Review Questions

A cubic unit is a cube whose edge measures 1 unit. Thus, a cubic inch is a cube whose edge is 1 in long. A parallelepiped is a prism bounded by six parallelograms (Fig. 17-5). Hence, the rectangular solid and cube are special parallelepipeds. The table that follows shows some relationships among polygons in plane geometry and the corresponding relationships among polyhedra in solid geometry. Plane Geometry Solid Geometry Polyhedron Polygon Quadrilateral Prism Parallelogram Parallelepiped Rectangle Square Rectangular solid Cube Pyramids A pyramid is a polyhedron whose base is a polygon and whose other faces meet at a point, its vertex. The base (B in Fig. 17-6) may have any number of sides. However, the other faces must be triangles. The distance from the vertex to the base is equal to the measure of the altitude or height h, a line from the vertex at a right angle to the base.

What is wrong with the following loop:

B Regular Pyramid (square base)

while (n <= 100) sum += n*n;

Fig. 17-6

If s is a compound statement, and el, e2, and e3 are expressions, then what is the difference between the program fragment:

Dim i1 As Integer, i2 As Integer, i3 As Integer, i4 As Integer i1 = . . . . . i2 = . . . . . i3 = . . . . . i4 = . . . . . . . . . . Call Reorder(i1, i2, i3, i4)

A regular pyramid is a pyramid whose base is a regular polygon and whose altitude joins the vertex and the center of the base. A frustum of a pyramid is the part of a pyramid that remains if the top of the pyramid is cut off by a plane parallel to the base. Note in Fig. 17-6 that its lateral faces are trapezoids. Cones A circular cone (Fig. 17-7) is a solid whose base is a circle and whose lateral surface comes to a point. (A circular cone is usually referred to simply as a cone.)

for (el; e2; e3) s;

Fig. 17-7

and the fragment:

el; while (e2) s; e3 ; > 3.4 {