Question

An opaque pyramid (shown below), with a square base and isosceles faces, is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The pyramid can be reoriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT possible? \begin{center} \includegraphics[width=0.5\textwidth]{03.jpeg} \end{center}

• A. P
• B. Q
• C. R
• D. S

Hint:

For shadow problems, always think about orthographic projections. A pyramid can project into triangles, trapeziums, pentagons, or a square, but not into an incomplete square with one side missing.

Answer 1

The Correct Option is A

Step 1: Shape of the pyramid.
The pyramid has a square base and 4 isosceles triangular faces, all meeting at the apex.

Step 2: Possible projections.
- When light is along the axis (top view), the shadow will be a square (like option S).
- When light is at an angle that highlights two adjacent triangular faces and the apex, the shadow will be a pentagon (like option R).
- When the pyramid is tilted further, the shadow can appear as an irregular quadrilateral (like option Q).

Step 3: Checking option P.
Shadow P shows a square with one clean cut side. Such a shape cannot occur because: - The pyramid has a pointed apex, so any tilted shadow must taper, not produce a flat "chopped" edge like in P. - The square base projection can only appear as a full square (S), not a partial irregular square like P.

Step 4: Conclusion.
Thus, shadow P is not possible. \[ \boxed{\text{P is not possible.}} \]