Let's solve the questions based on the information given in the image.

Given Data

1. Cuboid A:

   • Dimensions: $8 \, \text{cm} \times 12 \, \text{cm} \times 20 \, \text{cm}$
   • Volume $V_A = 8 \times 12 \times 20 = 1920 \, \text{cm}^3$

2. Cuboid B:

   • Dimensions: $8 \, \text{cm} \times 6 \, \text{cm} \times 12 \, \text{cm}$
   • Volume $V_B = 8 \times 6 \times 12 = 576 \, \text{cm}^3$

Part (i): How many cuboids B can be cut from cuboid A?

To find out how many cuboids B can fit into cuboid A, we divide the volume of Cuboid A by the volume of Cuboid B: $\text{Number of cuboids B} = \frac{1920}{576} = 3.33$ Since only whole cuboids can be cut, we can fit a maximum of 3 cuboids B into cuboid A.

Answer: 3 cuboids B

Part (ii): Calculate the volume of the small cuboid left over.

To find the leftover volume, we calculate the total volume of 3 cuboids B and subtract it from the volume of cuboid A: $\text{Volume of 3 cuboids B} = 3 \times 576 = 1728 \, \text{cm}^3$ $\text{Remaining volume} = 1920 - 1728 = 192 \, \text{cm}^3$

Answer: $192 \, \text{cm}^3$

Would you like further details on any step, or do you have additional questions?

Follow-up Questions:

1. How would the solution change if Cuboid B had different dimensions?
2. What if cuboid A had smaller dimensions? How many cuboids B could fit then?
3. How can we calculate the exact dimensions of the leftover cuboid?
4. Could we maximize the number of smaller cuboids by re-arranging cuts differently?
5. What if Cuboid B had a different orientation?

Tip: When dividing volumes to find the number of smaller cuboids fitting into a larger one, always remember to round down to ensure that only full cuboids are counted.