GCAT Spatial Visualization Tasks 5 — Questions and Answers
Question 1: A rectangular piece of paper 8×11 inches is rolled into a cylinder along its long edge. What is the approximate circumference of the resulting cylinder?
- 8 inches (Correct answer)
- 11 inches
- 16 inches
- 22 inches
Correct answer: 8 inches
Rolling along the long edge means the short edge (8 inches) becomes the circumference of the cylinder.
Question 2: Two identical right triangles are placed together along their hypotenuses. What shape is formed?
- A larger right triangle
- A rectangle (Correct answer)
- A parallelogram
- A trapezoid
Correct answer: A rectangle
Two congruent right triangles placed hypotenuse-to-hypotenuse form a rectangle.
Question 3: A cube is sliced diagonally through four of its edges (not faces). The cross-section is a rectangle. If the cube has side length 2, what is the area of the cross-section?
- 4
- 4√2 (Correct answer)
- 8
- 2√2
Correct answer: 4√2
A diagonal slice through a cube of side 2 produces a rectangle measuring 2 × 2√2, giving area 4√2.
Question 4: Which of the following objects would cast a triangular shadow when lit from directly above?
- A sphere
- A cone
- A triangular prism lying on a rectangular face (Correct answer)
- A cylinder
Correct answer: A triangular prism lying on a rectangular face
A triangular prism lying on a rectangular face has a triangular top face that casts a triangular shadow from directly above.
Question 5: A regular hexagon is divided into equilateral triangles by drawing lines from each vertex to the center. How many triangles are formed?
- 4
- 6 (Correct answer)
- 8
- 12
Correct answer: 6
Drawing lines from each of a hexagon's 6 vertices to its center creates exactly 6 equilateral triangles.
Question 6: An ant walks along the outside of a cube from one corner to the diagonally opposite corner. The cube has side length 1. What is the shortest path the ant can walk?
- √5 (Correct answer)
- √6
- 2
- 3
Correct answer: √5
Unfolding two adjacent faces into a 2×1 rectangle, the straight-line distance across is √(1² + 2²) = √5.
Question 7: A pattern of tiles uses only squares and regular octagons with equal side lengths, fitting together without gaps. How many sides does each octagon share with squares?
- 2
- 4 (Correct answer)
- 6
- 8
Correct answer: 4
In the standard square-octagon tiling, each octagon shares 4 of its 8 sides with squares (alternating sides).
GCAT Spatial Visualization Tasks 5
A rectangular piece of paper 8×11 inches is rolled into a cylinder along its long edge.
What is the approximate circumference of the resulting cylinder?