Calculate Cube Volume: Fitting 8 cm³ Blocks into an 84 cm³ Container

Q: Why can't I fit 11 cubes if I get 10.5?

Because you need entire cubes! The 0.5 represents only half of an 8 cm³ cube, which means there's only 4 cm³ of space left. You can't fit a whole 8 cm³ cube in that remaining space.

Q: How do I know when to round up or down?

For fitting problems, always round down. You can only count complete objects that fit entirely. Rounding up would mean trying to squeeze in more than the container can hold!

Q: What happens to the leftover space?

After fitting 10 cubes (80 cm³), you have 4 cm³ of leftover space (84 - 80 = 4). This space exists but isn't enough for another complete 8 cm³ cube.

Q: Can I use this method for any volume division problem?

Yes! The formula $ \frac{\text{Total Volume}}{\text{Small Object Volume}} $ works for any packing problem. Just remember to round down for whole objects.

Q: What if the division gives me a whole number?

Perfect! That means the smaller cubes fit exactly with no leftover space. For example, if you had 80 cm³ ÷ 8 cm³ = 10 exactly, all 10 cubes would fit perfectly.

Volume Division with Integer Containers

A cube has a volume of 84 cm3.

How many entire 8 cm³ cubes can fit inside the given cube?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 How many cubes can be fully placed inside the cube?

00:03 Let's calculate the volume ratio between the cubes

00:07 Let's break down 84 into 80 plus 4

00:13 Let's find a common denominator for all factors

00:17 We can see that we can fit 10 whole ones and a half

00:21 The cube cannot be split, therefore we can fit 10

00:24 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A cube has a volume of 84 cm3.

How many entire 8 cm³ cubes can fit inside the given cube?

Step-by-step solution

To solve this problem, we need to determine how many smaller cubes with a volume of 8 cm³ can fit inside a larger cube with a volume of 84 cm³.

We use the formula:

Number of smaller cubes $n = \frac{\text{Volume of the large cube}}{\text{Volume of the smaller cube}}$ .

Substituting the given volumes:

$n = \frac{84 \text{ cm}^3}{8 \text{ cm}^3} = 10.5$ .

Since we can only fit entire cubes, we round down to the nearest whole number. Therefore, the number of entire 8 cm³ cubes that can fit is 10.

Therefore, the solution to the problem is $10$ .

Final Answer

$10$

Key Points to Remember

Essential concepts to master this topic

Division Rule: Total volume divided by small cube volume gives maximum count
Technique: Calculate $\frac{84}{8} = 10.5$ then round down to 10
Check: Verify 10 × 8 = 80 cm³ fits, but 11 × 8 = 88 cm³ exceeds 84 cm³ ✓

Common Mistakes

Avoid these frequent errors

Rounding up instead of down for partial results
Don't round 10.5 up to 11 cubes = trying to fit 88 cm³ in 84 cm³! This exceeds the container capacity and is physically impossible. Always round down when dealing with entire objects that must fit completely.

Practice Quiz

Test your knowledge with interactive questions

A cube has a total of 14 edges.

FAQ

Everything you need to know about this question

Why can't I fit 11 cubes if I get 10.5?

Because you need entire cubes! The 0.5 represents only half of an 8 cm³ cube, which means there's only 4 cm³ of space left. You can't fit a whole 8 cm³ cube in that remaining space.

How do I know when to round up or down?

For fitting problems, always round down. You can only count complete objects that fit entirely. Rounding up would mean trying to squeeze in more than the container can hold!

What happens to the leftover space?

After fitting 10 cubes (80 cm³), you have 4 cm³ of leftover space (84 - 80 = 4). This space exists but isn't enough for another complete 8 cm³ cube.

Can I use this method for any volume division problem?

Yes! The formula $\frac{\text{Total Volume}}{\text{Small Object Volume}}$ works for any packing problem. Just remember to round down for whole objects.

What if the division gives me a whole number?

Perfect! That means the smaller cubes fit exactly with no leftover space. For example, if you had 80 cm³ ÷ 8 cm³ = 10 exactly, all 10 cubes would fit perfectly.

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