Question
In a model of a building, if the height is twice as tall as the width and the base has a length of 10 meters, what is the volume of the model?
Ask by Brooks Beck. in Nigeria
Jan 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The volume of the model building is 2,000 cubic meters.
Solution
To determine the volume of the model building, let's break down the given information and make some reasonable assumptions:
1. **Base Dimensions:**
- **Length (L):** 10 meters
- **Width (W):** Not explicitly given, but we'll assume the base is rectangular.
2. **Height (H):**
- It's stated that the height is twice as tall as the width, so:
\[
H = 2 \times W
\]
3. **Assumption:**
- Since the width isn't provided, a common assumption is that the base is square. This means:
\[
W = L = 10 \text{ meters}
\]
- Therefore, the height would be:
\[
H = 2 \times 10 = 20 \text{ meters}
\]
4. **Volume Calculation:**
- The volume \( V \) of a rectangular prism (which we'll assume the building is) is calculated as:
\[
V = L \times W \times H
\]
- Substituting the known values:
\[
V = 10 \times 10 \times 20 = 2000 \text{ cubic meters}
\]
**Final Answer:**
The volume of the model building is **2,000 m³**.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Bonus Knowledge
To find the volume of the model, we can use the formula for the volume of a rectangular prism: Volume = length × width × height. In this case, you've stated the length is 10 meters. If the width is \( w \), then the height is \( 2w \). First, we can represent the volume \( V \) as: \[ V = 10 \text{ m} \times w \times 2w = 20w^2 \] To calculate the volume, we need a value for \( w \). Without that, we can express the volume in terms of \( w \); just know that the volume increases significantly as the width gets larger! Additionally, if you have a specific width, just plug that number into the formula to get the exact volume!
