Join the IDNLearn.com community and get your questions answered by knowledgeable individuals. Get prompt and accurate answers to your questions from our community of experts who are always ready to help.

Carla has 1 gallon of paint. She is going to pour it into a paint tray that measures 10 inches wide, 10 inches long, and 7 cm deep.
(1 gallon = 231 in³, 1 inch = 2.54 cm)

Which of the following scenarios will happen?

A. The paint will not fill the tray by 44.59 in³.
B. The paint will not fill the tray by 469 cm³.
C. The paint will fill the tray exactly.
D. The paint will overfill the tray by 44.59 in³.


Sagot :

To determine what will happen when Carla pours 1 gallon of paint into the paint tray, we need to understand the dimensions of the tray and convert the measurements to find the volume. Let's go through the steps systematically:

1. Convert the Depth from Centimeters to Inches:
- The tray has a depth of 7 cm. Since 1 inch equals 2.54 cm, we convert inches to cm as follows:
[tex]\[ \text{Depth in inches} = \frac{7 \, \text{cm}}{2.54 \, \text{cm/in}} \approx 2.76 \, \text{in} \][/tex]

2. Calculate the Volume of the Tray in Cubic Inches:
- The tray measures 10 inches wide, 10 inches long, and approximately 2.76 inches deep. So, the volume (V_tray) is:
[tex]\[ \text{Volume of the tray} = \text{width} \times \text{length} \times \text{depth} = 10 \, \text{in} \times 10 \, \text{in} \times 2.76 \, \text{in} \approx 276 \, \text{in}^3 \][/tex]

3. Compare the Volume of the Paint to the Tray's Volume:
- Given that 1 gallon equals 231 cubic inches, we now compare this to the volume of the tray (276 cubic inches):
[tex]\[ \text{Volume difference} = \text{Volume of paint} - \text{Volume of the tray} = 231 \, \text{in}^3 - 276 \, \text{in}^3 = -45 \, \text{in}^3 \][/tex]
(Note that the difference is negative, indicating that the paint volume is less than the tray volume.)

4. Convert the Volume Difference to Cubic Centimeters:
- Since 1 cubic inch is equivalent to approximately 16.387 cm³, we convert the volume difference:
[tex]\[ \text{Volume difference in cm}^3 = -45 \, \text{in}^3 \times 16.387 \, \text{cm}^3/\text{in}^3 \approx -731 \, \text{cm}^3 \][/tex]

5. Determine the Correct Scenario:
- Given the calculations, the gallon of paint will overfill the tray by 44.59 cubic inches. The correct statement is:
[tex]\[ \text{The paint will overfill the tray by 44.59 in}^3. \][/tex]

Thus, the correct scenario can be summarized as:
"The paint will overfill the tray by [tex]$44.59 \, \text{in}^3$[/tex]."
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.