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

A cube has a volume of 84 cm3.

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

Video Solution

Solution Steps

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 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 $10$ .