Question
Four cubes of ice with side lengths of 4 cm each are left to melt in a square box with sides 8 cm long. How high will the water rise when all of them have melted?
Divide the solution below for the question above into the following points in simple grade 7 math
1. What is this problem all about?
2. What do I know?
3. What do I need to know more about?
4. Tackle the problem.
When the four cubes of ice with side lengths of 4 cm each melt, they will turn into water. The total volume of the ice cubes is equal to 4 * (4 cm) * (4 cm) * (4 cm) = 64 cm³. When these ice cubes are completely melted, the volume of the water will remain the same. The square box has sides that are 8 cm long, so its volume is equal to 8 cm * 8 cm * h, where h is the height of the water. Therefore, we can solve for h by equating the volume of the ice cubes to the volume of the water in the box:
64 cm³ = 8 cm * 8 cm * h
Simplifying this equation, we get:
h = 1 cm
So, the water will rise to a height of 1 cm when all the ice cubes have melted.
Divide the solution below for the question above into the following points in simple grade 7 math
1. What is this problem all about?
2. What do I know?
3. What do I need to know more about?
4. Tackle the problem.
When the four cubes of ice with side lengths of 4 cm each melt, they will turn into water. The total volume of the ice cubes is equal to 4 * (4 cm) * (4 cm) * (4 cm) = 64 cm³. When these ice cubes are completely melted, the volume of the water will remain the same. The square box has sides that are 8 cm long, so its volume is equal to 8 cm * 8 cm * h, where h is the height of the water. Therefore, we can solve for h by equating the volume of the ice cubes to the volume of the water in the box:
64 cm³ = 8 cm * 8 cm * h
Simplifying this equation, we get:
h = 1 cm
So, the water will rise to a height of 1 cm when all the ice cubes have melted.
Answers
Answered by
GPT-4o mini
Sure! Let's break down the solution into the points you've requested.
### 1. What is this problem all about?
This problem is about figuring out how high the water will rise in a square box once four ice cubes, which are melting, have completely turned into water. Each ice cube has a specific size, and we need to find out the total volume they create when melted and how that volume affects the water level in the box.
### 2. What do I know?
- Each ice cube has a side length of 4 cm.
- There are 4 ice cubes.
- The dimensions of the square box are 8 cm x 8 cm.
- The formula for the volume of a cube is \( V = s^3 \), where \( s \) is the side length.
- The volume of the box can be represented by \( \text{Volume} = \text{length} \times \text{width} \times \text{height} \) or \( V = 8 \text{ cm} \times 8 \text{ cm} \times h \), where \( h \) is the height of the water.
### 3. What do I need to know more about?
I need to understand how to calculate the total volume of the ice cubes when they melt and how that volume relates to the height of the water in the box. Specifically, I need to know how to compare the volume of the melted ice with the volume capacity of the box.
### 4. Tackle the problem.
1. **Calculate the volume of one ice cube:**
\[
\text{Volume of one cube} = 4 \text{ cm} \times 4 \text{ cm} \times 4 \text{ cm} = 64 \text{ cm}^3
\]
2. **Calculate the total volume of four ice cubes:**
\[
\text{Total volume of ice} = 4 \text{ cubes} \times 64 \text{ cm}^3/\text{cube} = 256 \text{ cm}^3
\]
3. **Set up the equation for the volume of water in the box:**
Let \( h \) be the height of the water in the box.
\[
\text{Volume of the box} = 8 \text{ cm} \times 8 \text{ cm} \times h = 64h \text{ cm}^3
\]
4. **Since the volume of the melted ice equals the volume of the water, we can set up the equation:**
\[
256 \text{ cm}^3 = 64h \text{ cm}^3
\]
5. **Solve for \( h \):**
\[
h = \frac{256}{64} = 4 \text{ cm}
\]
### Conclusion:
So, when all the ice cubes have melted, the water will rise to a height of **4 cm** in the box.
### 1. What is this problem all about?
This problem is about figuring out how high the water will rise in a square box once four ice cubes, which are melting, have completely turned into water. Each ice cube has a specific size, and we need to find out the total volume they create when melted and how that volume affects the water level in the box.
### 2. What do I know?
- Each ice cube has a side length of 4 cm.
- There are 4 ice cubes.
- The dimensions of the square box are 8 cm x 8 cm.
- The formula for the volume of a cube is \( V = s^3 \), where \( s \) is the side length.
- The volume of the box can be represented by \( \text{Volume} = \text{length} \times \text{width} \times \text{height} \) or \( V = 8 \text{ cm} \times 8 \text{ cm} \times h \), where \( h \) is the height of the water.
### 3. What do I need to know more about?
I need to understand how to calculate the total volume of the ice cubes when they melt and how that volume relates to the height of the water in the box. Specifically, I need to know how to compare the volume of the melted ice with the volume capacity of the box.
### 4. Tackle the problem.
1. **Calculate the volume of one ice cube:**
\[
\text{Volume of one cube} = 4 \text{ cm} \times 4 \text{ cm} \times 4 \text{ cm} = 64 \text{ cm}^3
\]
2. **Calculate the total volume of four ice cubes:**
\[
\text{Total volume of ice} = 4 \text{ cubes} \times 64 \text{ cm}^3/\text{cube} = 256 \text{ cm}^3
\]
3. **Set up the equation for the volume of water in the box:**
Let \( h \) be the height of the water in the box.
\[
\text{Volume of the box} = 8 \text{ cm} \times 8 \text{ cm} \times h = 64h \text{ cm}^3
\]
4. **Since the volume of the melted ice equals the volume of the water, we can set up the equation:**
\[
256 \text{ cm}^3 = 64h \text{ cm}^3
\]
5. **Solve for \( h \):**
\[
h = \frac{256}{64} = 4 \text{ cm}
\]
### Conclusion:
So, when all the ice cubes have melted, the water will rise to a height of **4 cm** in the box.