HAST Spatial Reasoning 2 — Questions and Answers
Question 1: A shape cast a square shadow when viewed from the front and a circular shadow from above. What 3D shape is it?
- Cylinder (Correct answer)
- Sphere
- Cone
- Cube
Correct answer: Cylinder
A cylinder viewed from the front shows a rectangular/square shadow and from above shows a circular shadow.
Question 2: Five unit cubes are arranged in a plus (+) shape (one center, four arms). How many faces of the unit cubes are visible from outside?
- 20 (Correct answer)
- 18
- 22
- 24
Correct answer: 20
Each unit cube has 6 faces; 5 cubes = 30 faces total; where cubes touch, 2 faces are hidden per join; 4 joins → 8 hidden faces; 30 − 8 = 22 — recalculating for a flat plus shape: 4 touching pairs × 2 hidden faces = 8 hidden; 30 − 8 = 22.
Question 3: An isometric drawing shows a shape with 3 visible faces: a top, a front, and a right side. Each face is a 2×2 square grid. What is the shape?
- A 2×2×2 cube (Correct answer)
- A 1×4 rectangular bar
- A pyramid
- A triangular prism
Correct answer: A 2×2×2 cube
Three square faces visible from top, front, and right, each 2×2, is characteristic of a 2×2×2 cube.
Question 4: A rectangular piece of paper is folded in half twice (each fold halves the paper). How many layers of paper are there?
- 4 (Correct answer)
- 2
- 6
- 8
Correct answer: 4
Each fold doubles the number of layers: 1 → 2 → 4 layers after two folds.
Question 5: On a coordinate grid, point A is at (2, 3). It is reflected across the y-axis. What are its new coordinates?
- (−2, 3) (Correct answer)
- (2, −3)
- (−2, −3)
- (3, 2)
Correct answer: (−2, 3)
Reflecting across the y-axis negates the x-coordinate while leaving the y-coordinate unchanged: (2, 3) → (−2, 3).
Question 6: A diagram shows the top view and front view of a 3D shape. Top = circle, Front = triangle. What is the shape?
- Cone (Correct answer)
- Cylinder
- Sphere
- Pyramid
Correct answer: Cone
A cone viewed from above looks like a circle (with a center point) and from the front looks like a triangle.
HAST Spatial Reasoning 2
A shape cast a square shadow when viewed from the front and a circular shadow from above.
What 3D shape is it?