To determine how many pieces of cake can fit in the box, we need to calculate the volume of both the cake and the box, then divide the box's volume by the cake's volume.

Step 1: Calculate the volume of the cake

The formula for the volume of a rectangular prism (a box) is: $\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}$ For the cake:

• Length = 14 cm
• Width = 10 cm
• Height = 7 cm

The volume of one cake piece is: $\text{Volume of cake} = 14 \times 10 \times 7 = 980 \, \text{cm}^3$

Step 2: Calculate the volume of the box

For the box:

• Length = 33 cm
• Width = 26.5 cm
• Height = 8 cm

The volume of the box is: $\text{Volume of box} = 33 \times 26.5 \times 8 = 6960 \, \text{cm}^3$

Step 3: Determine how many cake pieces fit in the box

Now, divide the volume of the box by the volume of the cake to find out how many pieces can fit in the box: $\text{Number of pieces} = \frac{\text{Volume of box}}{\text{Volume of cake}} = \frac{6960}{980} \approx 7.1$

Since you can’t fit a fraction of a cake, 7 pieces can fit in the box.

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Would you like more details on this process or have any further questions?

5 Related Questions:

1. How can I maximize the number of cakes that fit if I rotate the pieces?
2. If I increase the box size, how would that affect the number of cakes?
3. What is the best packing arrangement to fit more pieces?
4. How does the shape of the box affect the number of cakes that can fit?
5. If the cakes were irregularly shaped, how would I calculate the fit?

Tip:

When calculating how many objects fit into a container, always compare their volumes first, but also consider how the objects will be arranged to avoid empty space.