ATDH - Admission Test for Dental Hygiene Perceptual Ability: 3D Forms Questions and Answers — Questions and Answers
Question 1: An object is constructed from identical, stacked cubes. No cubes are floating. The structure has a base that is 3 columns wide and 2 rows deep. The front-left column is 3 cubes high. The front-middle column is 2 cubes high. The front-right column is 1 cube high. The entire back row of columns is 1 cube high. How many total cubes are in the object?
- 10
- 12
- 9
- 11 (Correct answer)
Correct answer: 11
Calculate the number of cubes in each vertical column and sum them. The leftmost column is 3 cubes high and 2 deep (3 * 2 = 6). The middle column is 2 cubes high and 2 deep (2 * 2 = 4). The rightmost column is 1 cube high and 2 deep (1 * 2 = 2). The total number of cubes is 6 + 4 + 2 = 12.
Question 2: A square piece of paper is folded in half diagonally from the top-right corner to the bottom-left corner. Then, the resulting triangle is folded in half again along its line of symmetry. Two small circular holes are punched through all layers: one near the right-angle corner and one in the center of the longest edge. What pattern will be visible when the paper is fully unfolded?
- Four holes in a diamond pattern along the diagonals, and four holes in a square pattern in the center.
- Two holes on one diagonal and two holes on the other diagonal. (Correct answer)
- Four holes forming a square in the center of the paper.
- Two holes along the diagonal that was first folded.
Correct answer: Two holes on one diagonal and two holes on the other diagonal.
The first unfold mirrors the two holes across the second fold line, creating four holes on the half-folded triangular paper. The final unfold mirrors these four holes across the main diagonal. The hole near the right-angle corner will be mirrored to create two holes on one diagonal. The hole on the long edge will be mirrored to create two holes on the other diagonal. The final result is four holes total, with two on each of the paper's diagonals.
Question 3: A 3D object is constructed from 5 identical cubes. It consists of a 2x2 square base (4 cubes) with one additional cube placed on top of the front-left cube. Which of the following correctly describes the Front View and the Top View of this object?
- Front View: A 2x2 square. Top View: A 2x2 square.
- Front View: An 'L' shape, 2 cubes high on the left and 1 cube high on the right. Top View: An 'L' shape.
- Front View: An 'L' shape, 2 cubes high on the left and 1 cube high on the right. Top View: A 2x2 square. (Correct answer)
- Front View: A 2x1 vertical rectangle. Top View: A 2x2 square.
Correct answer: Front View: An 'L' shape, 2 cubes high on the left and 1 cube high on the right. Top View: A 2x2 square.
When viewed from the top, you see the complete 2x2 footprint of the base, so the Top View is a 2x2 square. When viewed from the front, the cube stacked on the front-left position makes the left column appear 2 cubes high, while the right column (which has no stacked cube) is only 1 cube high. This creates an 'L' shape.
Question 4: A 2D pattern in the shape of a cross is made of six squares. If it is folded into a cube, which face is always opposite the face labeled '3'? The pattern is arranged with four squares in a vertical line, labeled 1, 2, 3, 4 from top to bottom. A square labeled 'L' is to the left of square 2, and a square labeled 'R' is to the right of square 2.
- Face L
- Face 1 (Correct answer)
- Face 4
- Face R
Correct answer: Face 1
In this standard cross-shaped net, faces that are separated by one other face in a straight line will be opposite each other when folded. Face 1 is separated from Face 3 by Face 2. Therefore, Face 1 and Face 3 will be opposite. Similarly, Face L would be opposite Face R, and Face 2 would be opposite Face 4.
Question 5: You are presented with a 3D cube that has symbols on three visible faces: a solid circle on the top, a solid square on the front, and a solid triangle on the right side. Which of the following 2D patterns could be folded to form this exact cube?
- A pattern where the circle, square, and triangle are arranged sequentially in a single row.
- A pattern where the square is central, the circle is directly above it, and the triangle is directly to the left of it.
- A pattern where the square and circle are adjacent, but the triangle is adjacent to the circle instead of the square.
- A pattern where the square is central, the circle is directly above it, and the triangle is directly to the right of it. (Correct answer)
Correct answer: A pattern where the square is central, the circle is directly above it, and the triangle is directly to the right of it.
To form the described cube, the faces must be oriented correctly relative to each other. If the square is the front face, the circle must be able to fold into the top position, and the triangle must be able to fold into the right-side position. This requires both the circle and the triangle to be directly adjacent to the square in the unfolded pattern, in the correct 'up' and 'right' positions.
Question 6: Four angles are presented for comparison. Angle A is slightly smaller than a right angle. Angle B is a straight line. Angle C is very small and acute. Angle D is clearly obtuse, about halfway between a right angle and a straight line. What is the correct order of the angles from smallest to largest?
- C, A, D, B (Correct answer)
- A, C, D, B
- C, D, A, B
- B, D, A, C
Correct answer: C, A, D, B
Ordering by angle type is the first step. Acute angles are smallest, followed by right angles, then obtuse angles, and finally straight angles. Angle C (acute) is the smallest. Angle A (slightly less than 90°) is next. Angle D (obtuse, ~135°) is larger than A. Angle B (a straight line, 180°) is the largest. Thus, the correct order is C, A, D, B.
ATDH - Admission Test for Dental Hygiene Perceptual Ability: 3D Forms Questions and Answers
An object is constructed from identical, stacked cubes.
No cubes are floating.
The structure has a base that is 3 columns wide and 2 rows deep.
The front-left column is 3 cubes high.
The front-middle column is 2 cubes high.
The front-right column is 1 cube high.
The entire back row of columns is 1 cube high.
How many total cubes are in the object?