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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]."
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]."
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