An architect is designing a house. He wants the bedroom to have the dimensions of 10 ft by 4 ft by 7 ft. The architect doubles one dimension to create the den. Does that mean the den will have double the volume of the bedroom?
First, find the volume of the bedroom.
Solve on paper. Then check your work on Zearn.
The bedroom will be 
280
 ft3.
Good work!
Does doubling one dimension mean the den will have double the volume of the bedroom? Why or why not?
Does doubling one dimension mean the den will have double the volume of the bedroom? 
Yes


If he doubles one dimension, the den's volume will be 
exactly double
 the volume of the bedroom.
Excellent!
Now, find the volume of the den.
Solve on paper. Then check your work on Zearn.
The den will be 
 ft3.

Let's solve this step by step.

### 1. Finding the Volume of the Bedroom
The volume \( V \) of a rectangular room is given by the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]

For the bedroom:
- Length = 10 ft
- Width = 4 ft
- Height = 7 ft

Plugging in these values:
\[
V = 10 \times 4 \times 7 = 280 \text{ ft}^3
\]

The volume of the bedroom is indeed **280 ft³**.

### 2. Does Doubling One Dimension Double the Volume?
Yes, doubling one dimension while keeping the other two constant will double the volume. This is because volume is directly proportional to each dimension in the formula \( V = l \times w \times h \). Doubling one dimension doubles the total product.

### 3. Finding the Volume of the Den
Let's assume the architect doubles the length (from 10 ft to 20 ft) to create the den.

Now, the new volume \( V_{\text{den}} \) will be:
\[
V_{\text{den}} = 20 \times 4 \times 7
\]
Calculating this:
\[
V_{\text{den}} = 560 \text{ ft}^3
\]

So, the volume of the den will be **560 ft³**. 

Would you like to verify any specific part of this process or go through more related examples? 

### Additional Questions to Consider:
1. What would happen if the architect doubled the width or height instead of the length?
2. How would the volume change if all dimensions were doubled?
3. If the architect wanted the den to be three times as large, how many dimensions would need to be altered?
4. How would halving one dimension impact the volume of the room?
5. Could the same doubling effect be achieved by increasing two dimensions by smaller amounts instead of doubling one?

**Tip:** When calculating volume, always check if a single or multiple dimensions are changing, as this significantly affects the outcome.

An architect is designing a house. He wants the bedroom to have the dimensions of 10 ft by 4 ft by 7 ft. The architect doubles one dimension to create the den. Does that mean the den will have double the volume of the bedroom?

Explore how doubling one dimension of a bedroom (10 ft x 4 ft x 7 ft) impacts the volume to create a den. Learn about volume calculations for rectangular prisms and proportionality concepts, suitable for Grades 6-8.

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