2 identical metal cubes were placed in a rectangular container with height 15cm and base area of 800 cm^2. Water was then added to a height of 10cm. When another 6 metal cubes were added into the container, 50cm^3 of water overflowed. What is the volume of one metal cube?

Let's denote the volume of one metal cube as \( V_{\text{cube}} \).

### Step 1: Initial Water Volume
Initially, the height of water in the container is 10 cm, and the base area of the container is 800 cm². Therefore, the initial volume of water is:

\[
V_{\text{water\_initial}} = \text{Base Area} \times \text{Height of Water} = 800 \, \text{cm}^2 \times 10 \, \text{cm} = 8000 \, \text{cm}^3
\]

### Step 2: Effect of Adding 6 More Metal Cubes
When another 6 cubes are added (on top of the initial 2 cubes), 50 cm³ of water overflows. This suggests that the total volume displaced by the cubes, minus the volume already displaced by the first 2 cubes, caused the overflow. The volume of water displaced by all 8 cubes (2 original + 6 added) is equal to the combined volume of all the cubes:

\[
V_{\text{displaced}} = 8 \times V_{\text{cube}}
\]

Since adding 6 more cubes caused 50 cm³ of water to overflow, we know that the difference in water displacement between the volume of 2 cubes and 8 cubes is 50 cm³:

\[
8 \times V_{\text{cube}} - 2 \times V_{\text{cube}} = 50 \, \text{cm}^3
\]

\[
6 \times V_{\text{cube}} = 50 \, \text{cm}^3
\]

### Step 3: Solving for the Volume of One Cube
Now, we can solve for \( V_{\text{cube}} \):

\[
V_{\text{cube}} = \frac{50}{6} \, \text{cm}^3 \approx 8.33 \, \text{cm}^3
\]

Thus, the volume of one metal cube is approximately \( 8.33 \, \text{cm}^3 \).

---

Do you have any questions or want more details on any part of the solution?

Here are five related questions for further practice:
1. What would happen if 4 cubes were added instead of 6?
2. How much water would overflow if 10 cubes were added?
3. What is the height of water in the container if only one cube is added?
4. If the container's base area were changed to 1000 cm², how would the overflow change?
5. How many cubes in total would make the water overflow by 200 cm³?

**Tip**: When calculating volume displacement, always ensure that the displaced volume matches the object volume, and use careful tracking of overflow or other volume changes.

Solve the problem of finding the volume of a metal cube based on the water displaced in a container. In this scenario, 2 metal cubes are placed in a container, and after adding 6 more cubes, 50 cm³ of water overflows. Learn how to calculate the volume of one cube using volume displacement and algebra. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation