Calculating Volume of Rectangular Prisms — Solutions

1. Composite Base Area

   1. Large rectangle area (20 × 15): 300 cm² ▶ View Solution
   2. Cut-out area (10 × 4): 40 cm² ▶ View Solution
   3. Shaded base area: 260 cm² ▶ View Solution
   4. Volume (base 260, height 5): 1 300 cm³ ▶ View Solution

2. Find the Volume

   1. Prism (a): 5 × 3 × 4: 60 cm³ ▶ View Solution
   2. Prism (b): 8 × 3 × 2: 48 m³ ▶ View Solution
   3. Prism (c): 6.5 × 4 × 3: 78 cm³ ▶ View Solution
   4. Prism (d): 10 × 5 × 4: 200 mm³ ▶ View Solution
   5. Cube (e): 6 × 6 × 6: 216 cm³ — all sides equal so l × w × h = s × s × s = s³ ▶ View Solution

3. Counting the Layers

   1. Bottom layer (5 × 4): 20 blocks ▶ View Solution
   2. Base area: 20 cm² ▶ View Solution
   3. Number of layers: 3 ▶ View Solution
   4. Total volume: 60 cm³ ▶ View Solution

4. Base Area and Height

   1. Base area = 32, l = 8; width: 4 cm ▶ View Solution
   2. Volume (base 32, height 10): 320 cm³ ▶ View Solution
   3. Volume when height halved to 5: 160 cm³ — halving height halves volume ▶ View Solution
   4. Effect of doubling base area (height = 10): Volume doubles to 640 cm³ ▶ View Solution

5. Applying the Formula

   1. l = 10 cm, w = 6 cm, h = 8 cm ▶ View Solution
   2. Volume: 480 cm³ ▶ View Solution
   3. Volume when width tripled: 1 440 cm³ ▶ View Solution
   4. Top face area: 60 cm² ▶ View Solution

6. Special Case: The Cube

   1. Face area (side = 5 cm): 25 cm² ▶ View Solution
   2. Volume (side = 5 cm): 125 cm³ ▶ View Solution
   3. Volume (side = 10 cm): 1 000 cm³ ▶ View Solution
   4. How many 5 cm cubes fit in 10 cm cube: 8 ▶ View Solution

7. Working with Decimals

   1. Volume (6 × 2.5 × 2): 30 m³ ▶ View Solution
   2. 6 m in cm: 600 cm ▶ View Solution
   3. Volume when height halved to 1 m: 15 m³ ▶ View Solution
   4. 30 m³ in litres: 30 000 litres ▶ View Solution

8. Finding the Missing Dimension

   1. V = 200, base area = 40; height: 5 cm ▶ View Solution
   2. V = 84, l = 7, w = 3; height: 4 cm ▶ View Solution
   3. V = 27 (cube); side: 3 cm ▶ View Solution
   4. V = 150, h = 10; one valid set of l and w: e.g. l = 5 cm, w = 3 cm ▶ View Solution

9. The Aquarium

   1. Total volume (50 × 30 × 40): 60 000 cm³ ▶ View Solution
   2. Water volume (depth 25 cm): 37 500 cm³ ▶ View Solution
   3. More water needed to fill: 22 500 cm³ ▶ View Solution
   4. Current water in litres: 37.5 litres ▶ View Solution

10. Compound Prisms

    1. Lower block volume (60 × 30 × 20): 36 000 cm³ ▶ View Solution
    2. Upper block volume (30 × 30 × 20): 18 000 cm³ ▶ View Solution
    3. Total volume: 54 000 cm³ ▶ View Solution
    4. Cost at $0.05/cm³: $2 700 ▶ View Solution