Introduction to Prisms & Volume — Solutions

1. Is It a Prism?

   1. Cuboid: Yes — Rectangular prism ▶ View Solution
   2. Tapers to a point: No — Triangular pyramid (tetrahedron) ▶ View Solution
   3. Triangle cross-section: Yes — Triangular prism ▶ View Solution
   4. Curved surface: No — Cylinder ▶ View Solution
   5. Two hexagonal bases: Hexagonal prism ▶ View Solution

2. True or False?

   1. A cube is a special rectangular prism: True ▶ View Solution
   2. Cross-section of a triangular prism is a rectangle: False ▶ View Solution
   3. Volume is measured in cm²: False ▶ View Solution
   4. A square prism is a valid name: True ▶ View Solution
   5. A cylinder is a prism: False ▶ View Solution

3. Counting Unit Cubes

   1. 2 × 2 × 2: 8 cm³ ▶ View Solution
   2. 4 × 3 × 2: 24 cm³ ▶ View Solution
   3. 2 × 2 × 3: 12 cm³ ▶ View Solution
   4. Hidden from front (back 2 layers: 4 × 2 × 2): 16 hidden cubes ▶ View Solution
   5. 3 cubes per layer, 4 layers: 12 cm³ ▶ View Solution

4. Volume Formula Practice

   1. 5 × 3 × 2: 30 cm³ ▶ View Solution
   2. 8 × 4 × 3: 96 m³ ▶ View Solution
   3. 10 × 6 × 5: 300 cm³ ▶ View Solution
   4. 4 × 4 × 4: 64 cm³ ▶ View Solution
   5. 12 × 5 × 2: 120 mm³ ▶ View Solution

5. The Layer Method

   1. One layer (6 × 4): 24 cubes ▶ View Solution
   2. Total volume (24 cubes × 5 layers): 120 cm³ ▶ View Solution
   3. Layers if total = 100, base = 20: 5 layers ▶ View Solution
   4. Base area 18, height 7: 126 cm³ ▶ View Solution

6. Choosing the Right Unit

   1. Juice box: cm³ ▶ View Solution
   2. Swimming pool: m³ ▶ View Solution
   3. Grain of sand: mm³ ▶ View Solution
   4. School classroom: m³ ▶ View Solution

7. Volume and Capacity

   1. 600 cm³ in mL: 600 mL ▶ View Solution
   2. 30 000 cm³ in litres: 30 litres ▶ View Solution
   3. 3.5 L in cm³: 3 500 cm³ ▶ View Solution
   4. Container of 2 500 cm³ vs 2 L: More than 2 litres (holds 2.5 L) ▶ View Solution

8. Finding a Missing Dimension

   1. h = 2 cm ▶ View Solution
   2. w = 5 m ▶ View Solution
   3. s = 6 cm ▶ View Solution
   4. h = 3 cm ▶ View Solution

9. Filling the Pool

   1. Full pool volume (12 × 6 × 2): 144 m³ ▶ View Solution
   2. Volume at 1.5 m depth: 108 m³ ▶ View Solution
   3. Additional water needed: 36 m³ ▶ View Solution

10. Error Analysis and Reasoning

    1. Aisha’s error and correct answer (4 × 5 × 3): Used cm² instead of cm³; correct answer: 60 cm³ ▶ View Solution
    2. One valid set of dimensions for Box B (V = 48 cm³): e.g. 6 × 4 × 2 cm ▶ View Solution
    3. Original V = 60; height doubled; increase and effect: Increase = 60 cm³ — volume doubled ▶ View Solution