DAT Domain 2: Perceptual Ability Welcome to your DAT Domain 2: Perceptual Ability 1. DAT: Perceptual Ability A cube is painted red on all sides and then cut into smaller cubes of exactly the same size. If the original cube was divided into 27 smaller cubes, how many of these smaller cubes will have paint on two sides only? 6 8 12 18 None 2. DAT: Perceptual Ability Imagine unfolding a cube with a number on each face (1 to 6). If face 1 is opposite face 6, and face 2 is adjacent to faces 1, 3, 4, and 6, which face is opposite face 2? 3 4 5 None of the above None 3. DAT: Perceptual Ability When a pyramid with a square base is viewed directly from one side, what shape is seen? Triangle Square Rectangle Pentagon None 4. DAT: Perceptual Ability A cylindrical rod is cut into smaller sections. If the cuts are made perpendicular to the length of the rod, what shape are the faces of the sections? Squares Circles Rectangles Triangles None 5. DAT: Perceptual Ability How many lines of symmetry does an equilateral triangle have? 1 2 3 4 None 6. DAT: Perceptual Ability A rectangular prism is composed of smaller identical cubes. The prism measures 4 cubes in length, 3 cubes in height, and 2 cubes in width. How many cubes are visible if one corner cube is removed from the prism? 21 22 23 24 None 7. DAT: Perceptual Ability Consider a sphere with a single point marked on it. If the sphere is rotated around one of its diameters, how many distinct positions can the marked point occupy? 1 2 Infinite None None 8. DAT: Perceptual Ability Which of the following is not a possible net of a cube? Six squares arranged in a cross shape with four squares in a row and one each extending from the second and third squares of the row. Six squares arranged in a T-shape with three squares in a row and three connected squares extending downward from the middle square. Four squares in a row with one square attached to each of the squares at the ends. Four squares in a row with one square attached to the third square. None 9. DAT: Perceptual Ability A shape is formed by attaching a regular hexagon to one of the sides of a regular pentagon. How many sides does the resulting shape have? 10 11 9 12 None 10. DAT: Perceptual Ability If two identical triangles are overlaid such that they are rotated 180 degrees relative to each other about their centroids, what shape is most likely formed by their intersection? A smaller identical triangle A hexagon An octagon A square None 11. DAT: Perceptual Ability An octahedron has how many faces, vertices, and edges? 8 faces, 6 vertices, 12 edges 6 faces, 8 vertices, 12 edges 8 faces, 12 vertices, 6 edges 6 faces, 12 vertices, 8 edges None 12. DAT: Perceptual Ability When a complex 3D object composed of various geometric shapes is viewed from above, which observation is correct regarding the visibility of its bases? Only the highest base is visible. All bases are visible. No bases are visible. Only circular bases are visible. None 13. DAT: Perceptual Ability A mirror reflects a pyramid with a square base. If the mirror is placed parallel to the base and adjacent to one of its sides, how many total pyramids will be visible? 1 2 3 4 None 14. DAT: Perceptual Ability Three different-colored cubes are stacked vertically. If you view the stack from the side, how many colors are visible? 1 2 3 None None 15. DAT: Perceptual Ability A rectangular box is painted all over and then cut into smaller boxes, each 2x2x2 cm. If the original box measures 8x6x4 cm, how many of the smaller boxes will have paint on exactly three sides? 8 4 12 16 None 16. DAT: Perceptual Ability When looking at a complex diagram that includes a cube, a sphere, and a cone, if a light source is positioned directly above them, which shape will cast the smallest shadow? Cube Sphere Cone All will cast the same size shadow None 17. DAT: Perceptual Ability In an arrangement of various geometric solids, a cone, a cylinder, and a cube are positioned in a line. If a laser beam is directed at one end of the line at ground level, which solid will allow the beam to pass to the other side without obstruction? Cone Cylinder Cube None of them None 18. DAT: Perceptual Ability If a transparent cube has a smaller cube suspended in its center, how many faces of the smaller cube are visible from the outside? 3 4 5 6 None 19. DAT: Perceptual Ability When a 2D figure consisting of a triangle on top of a square is rotated about an axis passing through the center of the square and perpendicular to its plane, what 3D object is formed? Cylinder Cone Sphere Pyramid None 20. DAT: Perceptual Ability What is the minimum number of colors needed to paint a tetrahedron so that no two adjacent faces have the same color? 1 2 3 4 None 21. DAT: Perceptual Ability A solid cube is constructed by gluing together small identical cubes. If the solid has 6 layers and each layer is a 6x6 grid of small cubes, how many small cubes are on the surface of the large cube? 216 176 144 196 None 22. DAT: Perceptual Ability When viewing a 3D model of a structure composed of various interconnected cubes, how can you determine the number of cubes used if some cubes may be hidden from view? Count the visible cubes and estimate based on the gaps. Measure the total volume and divide by the volume of one cube. Count all visible faces, edges, and vertices to estimate. It is not possible to accurately determine without additional information. None 23. DAT: Perceptual Ability A three-dimensional shape is created by slicing a cylinder along a diagonal plane from the top edge to the bottom opposite edge. What shape is the cross-section? Circle Ellipse Rectangle Triangle None 24. DAT: Perceptual Ability In an arrangement of 10 stacked layers of spheres, with each layer directly above the other, what is the shape of the gaps formed between four adjacent spheres in any given layer? Triangular Square Tetrahedral Octahedral None 25. DAT: Perceptual Ability A solid is formed by attaching a cylinder to a cube such that the base of the cylinder rests entirely on one face of the cube. If the height of the cylinder is equal to the edge of the cube and the diameter of the cylinder is equal to the edge length of the cube, how many faces does the resulting solid have? 5 6 4 7 None 26. DAT: Perceptual Ability How many edges are shared between adjacent faces on a regular dodecahedron? 12 30 20 5 None 27. DAT: Perceptual Ability In a construction set, if five different-colored cubes are arranged in a single line, how many unique ways can these colors be ordered? 60 120 720 24 None 28. DAT: Perceptual Ability A pyramid with a square base is cut parallel to its base halfway up. What shape is the cross-section created by this cut? Square Triangle Rectangle Circle None 29. DAT: Perceptual Ability A regular hexagon is divided into six equilateral triangles by drawing lines from each vertex to the center. How many lines of symmetry does this new figure have? 6 12 3 9 None 30. DAT: Perceptual Ability If a solid cube is viewed through a planar mirror placed at a 45-degree angle to one of its faces, how many total cubes will appear to be present, including the reflection? 1 2 3 4 None 1 out of 30 Time is Up! Time's up
