An opaque cylinder (shown below) 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 cylinder 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?
To solve this problem, we need to determine which shadow shape is not possible for an opaque cylinder suspended in a parallel beam of light.
- When the cylinder is oriented with its circular face perpendicular to the beam of light, the shadow will be a circle. This corresponds to shadow P.
- If the cylinder is oriented with its curved face parallel to the light beam, the shadow will be a rectangle. This is represented by shadow R.
- If the cylinder is oriented at an angle to the beam of light, the shadow will be an ellipse. This corresponds to shadow Q.
- Shadow S has a shape like a parallelogram. A cylinder, being a symmetrical object with circular tops, cannot cast a shadow in the form of a parallelogram. This shape is not possible regardless of the cylinder's orientation.
Thus, the shadow shape S is not possible for the given configuration. The cylinder, due to its geometric properties, cannot cast a parallelogram shadow.
Important Questions from 2D 3D Pattern Visualization
Three different views of a dice are shown in the figure below.
The piece of paper that can be folded to make this dice is
- Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting plane passes through the vertices of the assembled cones, what shape does the outer boundary of the resulting cross-section make?
Five cubes of identical size and another smaller cube are assembled as shown in Figure A. If viewed from direction X, the planar image of the assembly appears as Figure B.
If viewed from direction Y, the planar image of the assembly (Figure A) will appear asA palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters.
From the additional plates given in the options, which one of the combinations of additional plates would allow the player to construct a five-letter palindrome. The player should use all the five plates exactly once. The plates can be rotated in their plane.
The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.
What is the maximum number of squares without a "hole in the interior" that can be formed within the 4 × 4 grid using the unit squares as building blocks?
