Texas Civil Service Exam Mechanical and Spatial Aptitude 3 — Questions and Answers
Question 1: If you look at a 3D object from above (top view) and see a circle, and from the front you see a rectangle, the object is most likely a:
- Cone
- Sphere
- Cylinder (Correct answer)
- Pyramid
Correct answer: Cylinder
A cylinder appears as a circle from the top and a rectangle from the front.
Question 2: Two gears are meshed together. Gear A has 20 teeth and Gear B has 60 teeth. If Gear A rotates at 90 RPM, how fast does Gear B rotate?
- 270 RPM
- 90 RPM
- 30 RPM (Correct answer)
- 45 RPM
Correct answer: 30 RPM
Gear ratio = 20/60 = 1/3, so Gear B rotates at 90 × (1/3) = 30 RPM.
Question 3: A hydraulic jack has an input piston with an area of 2 sq inches and an output piston with an area of 20 sq inches. A 10-pound force on the input produces how much output force?
- 10 pounds
- 50 pounds
- 100 pounds (Correct answer)
- 200 pounds
Correct answer: 100 pounds
Pascal's Law: output force = input force × (output area / input area) = 10 × (20/2) = 100 pounds.
Question 4: A block slides down a ramp inclined at 30°. Which force component pulls the block down the slope?
- The full weight of the block
- Weight × cos(30°)
- Weight × sin(30°) (Correct answer)
- Weight × tan(30°)
Correct answer: Weight × sin(30°)
The component of gravity along a slope equals weight × sin(angle), which is the force pulling the block down the ramp.
Question 5: A net is folded into a 3D shape. The net has one square and four triangles arranged around it. What shape does it form?
- Cube
- Rectangular prism
- Square pyramid (Correct answer)
- Triangular prism
Correct answer: Square pyramid
One square base with four triangular faces folding upward forms a square pyramid.
Question 6: Which simple machine is essentially an inclined plane wrapped around a cylinder?
- Lever
- Pulley
- Wedge
- Screw (Correct answer)
Correct answer: Screw
A screw is an inclined plane (ramp) wrapped helically around a cylinder, converting rotational force into linear force.
Question 7: A spring stretches 3 inches under a 6-pound load. According to Hooke's Law, how far will it stretch under a 10-pound load?
- 3 inches
- 4 inches
- 5 inches (Correct answer)
- 6 inches
Correct answer: 5 inches
Spring constant k = 6/3 = 2 lb/in; stretch = 10/2 = 5 inches.
Texas Civil Service Exam Mechanical and Spatial Aptitude 3
If you look at a 3D object from above (top view) and see a circle, and from the front you see a rectangle, the object is most likely a: