<p>This is from an old PSAT: </p>
<p>The surface of a 3-dimensional solid consists of faces, each of which has the shape of a polygon. What is the least number of faces that the solid can have?</p>
<p>A. 2
B. 3
C. 4
D. 5
E. 6</p>
<p>I'm really bad at these "imagine" questions... so can someone please help? Thanks</p>
<p>C, 4 sides.. which polygon with least sides? Triangle. A pyramid, with 3 upper faces and 1 bottom face.</p>
<p>I think it's 4?</p>
<p>Think of all the 3-D shapes you have ever learned about. How many sides did they have?</p>
<p>Triangular Pyramid - 4
Pyramid - 5
Cube - 6</p>
<p>It seems they don't have any less faces than 4... though I may be wrong. </p>
<p>Or maybe, think: what's the simplest polygon? A triangle. What's the simplest solid you can make from triangles? A triangular pyramid.</p>
<p>I think it is C. </p>
<p>First think of the polygon with the least amount of sides-- a triangle, right? That's 3 sides and you can't go any lower than 3 and still have a polygon.</p>
<p>Next, think of a polygon with all triangles-- a triangular pyramid. </p>
<p>So, a triangular pyramid has 4 faces.</p>
<p>Since you can't visualize it, just draw it out on the scratch paper. I find it easier to start from the base of the figure. :) Hope this helped!</p>
<p>The polygon with the fewest sides is a triangle. So imagine a triangle, and that triangle needs to be connected by other faces so that it becomes three dimensional. There are 3 edges to the triangle, and you need one face for each side, that gives you 3 more faces. Those 3 faces can meet up at one point (i.e. form a pyramid) and so you have four faces total.</p>
<p>thanks for explaining in more detail what i said mulberrypie and dchow, i now see that my explanation was rushed lol ...</p>
<p>Haha, it was totally unintentional. When I started replying there were no replies, but when I actually pressed 'Submit' everyone had already answered. :P</p>
<p>thanks you guys!</p>
<p>Definitely C (4)</p>
<p>the polygon with the least number of sides is a triangle; and a triangular pyramid (triangles with base of triangle) will yield the 3D object with the least number of faces. Hope that helps</p>
<p>Variation:
What's the least number of planes that can "meet" in one point (vertex)? Three. Add one more plane to intersect these three, and you get space limited by four planes - four faces that is.</p>