https://file.aiquickdraw.com/mathbot/file/1726136254759qeaa90g2.jpg

Let's solve this problem step-by-step.

### Part (a) - Converting Volume to Cubic Meters

To convert the volume of paint from U.S. gallons to cubic meters, we use the conversion factor:

\[
1 \text{ U.S. gallon} = 0.00378541 \text{ cubic meters (m}^3\text{)}
\]

Given the paint volume of \(0.686\) U.S. gallons, we convert it to cubic meters:

\[
\text{Volume in cubic meters} = 0.686 \times 0.00378541
\]

### Part (b) - Calculating the Thickness of Wet Paint Layer

If all the remaining paint is used to coat a wall evenly, we need to determine the thickness \( t \) of the wet paint layer.

The formula for thickness is:

\[
\text{Thickness} = \frac{\text{Volume of Paint}}{\text{Area of the Wall}}
\]

Given:
- Wall area = \(11.6 \, \text{m}^2\)

So,

\[
t = \frac{\text{Volume in cubic meters}}{11.6}
\]

Now, let's calculate these values.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can guide you through the calculations step-by-step so you can solve it yourself:

### Part (a) - Convert Volume to Cubic Meters

1. Use the conversion factor:  
   \[
   1 \text{ U.S. gallon} = 0.00378541 \text{ cubic meters}
   \]
2. Multiply the given volume by this conversion factor:  
   \[
   \text{Volume in cubic meters} = 0.686 \times 0.00378541 \approx 0.002597 \, \text{m}^3
   \]

### Part (b) - Calculate the Thickness of Wet Paint Layer

1. Use the formula for thickness:  
   \[
   \text{Thickness} = \frac{\text{Volume of Paint}}{\text{Area of the Wall}}
   \]
2. Substitute the values:  
   \[
   \text{Thickness} = \frac{0.002597}{11.6} \approx 0.000224 \, \text{m}
   \]

Thus, the thickness of the layer is approximately 0.000224 meters or 0.224 millimeters.

Would you like to go into more detail, or do you have any other questions?

### Related Questions:

1. How do you convert between different volume units?
2. What are some practical applications of these calculations in real life?
3. How can you calculate the amount of paint needed to coat surfaces of different sizes?
4. What is the difference between U.S. gallons and Imperial gallons?
5. How can you calculate the cost of painting a wall based on paint coverage?

### Tip:
Always double-check unit conversions, especially when working with different measurement systems like U.S. customary units and the metric system.

A partly-full paint can has 0.686 U.S. gallons of paint left in it. (a) What is the volume of the paint, in cubic meters? (b) If all the remaining paint is used to coat a wall evenly (wall area = 11.6 m^2), how thick is the layer of wet paint? Give your answer in meters.

Learn how to convert 0.686 U.S. gallons of paint to cubic meters and calculate the thickness of a wet paint layer when applied to an 11.6 m² wall. This problem covers unit conversions and basic geometry, suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation