GAT Geometry and Spatial 1 — Questions and Answers
Question 1: A triangular plot of land has a base of 20 meters and a height of 15 meters. What is its area?
- 100 m²
- 150 m² (Correct answer)
- 200 m²
- 300 m²
Correct answer: 150 m²
Area of a triangle = (1/2) × base × height = (1/2) × 20 × 15 = 150 m². Triangle area calculations are essential for the Qudurat quantitative section.
Question 2: A cube has a side length of 5 cm. What is its total surface area?
- 25 cm²
- 125 cm²
- 150 cm² (Correct answer)
- 625 cm²
Correct answer: 150 cm²
A cube has 6 identical square faces. Surface area = 6 × side² = 6 × 5² = 6 × 25 = 150 cm².
Question 3: If two angles of a triangle measure 45° and 65°, what is the third angle?
- 60°
- 70° (Correct answer)
- 80°
- 90°
Correct answer: 70°
The sum of angles in a triangle = 180°. Third angle = 180° - 45° - 65° = 70°.
Question 4: What is the volume of a cylinder with radius 3 cm and height 10 cm? (Use π ≈ 3.14)
- 94.2 cm³
- 188.4 cm³
- 282.6 cm³ (Correct answer)
- 314 cm³
Correct answer: 282.6 cm³
Volume = πr²h = 3.14 × 3² × 10 = 3.14 × 9 × 10 = 282.6 cm³. Cylinder volume combines circle area with height.
Question 5: A rectangular prism has dimensions 4 cm × 6 cm × 8 cm. What is its volume?
- 96 cm³
- 144 cm³
- 192 cm³ (Correct answer)
- 288 cm³
Correct answer: 192 cm³
Volume = length × width × height = 4 × 6 × 8 = 192 cm³.
Question 6: If a square is inscribed in a circle of radius 5 cm, what is the side length of the square?
- 5 cm
- 5√2 cm (Correct answer)
- 10 cm
- 10/√2 cm
Correct answer: 5√2 cm
When a square is inscribed in a circle, the diagonal of the square equals the diameter = 2×5 = 10 cm. Side = diagonal/√2 = 10/√2 = 5√2 cm ≈ 7.07 cm.
GAT Geometry and Spatial 1
A triangular plot of land has a base of 20 meters and a height of 15 meters.
What is its area?