Question
The volume of a rectangular prism can be calculated with the formula V=lwh
, where V
is the volume, l
is the length, w
is the width, and h
is the height. If a rectangular prism has a volume of 90 ft.3
, length of 3 ft., and height of 12 ft., what is its width? Enter your answer as a decimal.(1 point)
ft.
, where V
is the volume, l
is the length, w
is the width, and h
is the height. If a rectangular prism has a volume of 90 ft.3
, length of 3 ft., and height of 12 ft., what is its width? Enter your answer as a decimal.(1 point)
ft.
Answers
GPT-4o mini
To find the width of the rectangular prism, we can use the volume formula:
\[ V = l \times w \times h \]
We know:
- \( V = 90 \, \text{ft}^3 \)
- \( l = 3 \, \text{ft} \)
- \( h = 12 \, \text{ft} \)
We need to solve for \( w \):
\[ 90 = 3 \times w \times 12 \]
First, calculate \( 3 \times 12 \):
\[ 3 \times 12 = 36 \]
Now we can rewrite the equation:
\[ 90 = 36 \times w \]
To isolate \( w \), divide both sides by 36:
\[ w = \frac{90}{36} \]
Now simplify the fraction:
\[ w = \frac{90 \div 18}{36 \div 18} = \frac{5}{2} = 2.5 \]
Therefore, the width \( w \) is:
\[ \boxed{2.5} \, \text{ft} \]
\[ V = l \times w \times h \]
We know:
- \( V = 90 \, \text{ft}^3 \)
- \( l = 3 \, \text{ft} \)
- \( h = 12 \, \text{ft} \)
We need to solve for \( w \):
\[ 90 = 3 \times w \times 12 \]
First, calculate \( 3 \times 12 \):
\[ 3 \times 12 = 36 \]
Now we can rewrite the equation:
\[ 90 = 36 \times w \]
To isolate \( w \), divide both sides by 36:
\[ w = \frac{90}{36} \]
Now simplify the fraction:
\[ w = \frac{90 \div 18}{36 \div 18} = \frac{5}{2} = 2.5 \]
Therefore, the width \( w \) is:
\[ \boxed{2.5} \, \text{ft} \]
The area of a rectangle is calculated with the formula A=lw. If the area of a rectangle is 52.5 m2 and the width is 5 m, what is the length? Explain the solution to the real-world problem.(1 point)
Responses
The length is 10.5 m.
The length is 10.5 m.
The length is 262.5 m2.
The length is 262.5 m squared .
l=10.5
l equals 10.5
The length is 262.5 m.
Responses
The length is 10.5 m.
The length is 10.5 m.
The length is 262.5 m2.
The length is 262.5 m squared .
l=10.5
l equals 10.5
The length is 262.5 m.
GPT-4o mini
To find the length of a rectangle given the area and the width, we can use the formula for the area of a rectangle:
\[ A = l \times w \]
where:
- \( A \) is the area,
- \( l \) is the length,
- \( w \) is the width.
In this case, we are given:
- \( A = 52.5 \, \text{m}^2 \)
- \( w = 5 \, \text{m} \)
We need to solve for \( l \):
1. Plug the values into the formula:
\[ 52.5 = l \times 5 \]
2. To isolate \( l \), divide both sides by 5:
\[ l = \frac{52.5}{5} \]
3. Calculate \( l \):
\[ l = 10.5 \, \text{m} \]
So, the length \( l \) is \( 10.5 \, \text{m} \).
### Explanation of the Solution:
In the context of a real-world problem, if we think about a rectangular garden that has an area of 52.5 square meters and a width of 5 meters, we can determine that the length of the garden must be 10.5 meters to achieve that area. This information can help a gardener or planner know exactly how much length is needed to fit the desired area for planting.
The correct response is:
**The length is 10.5 m.**
\[ A = l \times w \]
where:
- \( A \) is the area,
- \( l \) is the length,
- \( w \) is the width.
In this case, we are given:
- \( A = 52.5 \, \text{m}^2 \)
- \( w = 5 \, \text{m} \)
We need to solve for \( l \):
1. Plug the values into the formula:
\[ 52.5 = l \times 5 \]
2. To isolate \( l \), divide both sides by 5:
\[ l = \frac{52.5}{5} \]
3. Calculate \( l \):
\[ l = 10.5 \, \text{m} \]
So, the length \( l \) is \( 10.5 \, \text{m} \).
### Explanation of the Solution:
In the context of a real-world problem, if we think about a rectangular garden that has an area of 52.5 square meters and a width of 5 meters, we can determine that the length of the garden must be 10.5 meters to achieve that area. This information can help a gardener or planner know exactly how much length is needed to fit the desired area for planting.
The correct response is:
**The length is 10.5 m.**