Question
The density of a certain material is such that it weighs 9 kilograms for every 10 quarts of volume. Express this density in ounces per cubic foot. Round your answer to the nearest whole number.
*Note: you must use these exact conversion factors to get this question right.
Weight / mass Volume
1 pound left parenthesis, lb, right parenthesis(lb) = 16 ounces left parenthesis, oz, right parenthesis(oz) 1 cup left parenthesis, cup, right parenthesis(cup) = 8 fluid ounces left parenthesis, fl oz, right parenthesis(fl oz)
1 ton left parenthesis, ton, right parenthesis(ton) = 2000 pounds left parenthesis, lb, right parenthesis(lb) 1 pint left parenthesis, pt, right parenthesis(pt) = 2 cups left parenthesis, cups, right parenthesis(cups)
1 gram left parenthesis, g, right parenthesis(g) = 1000 milligrams left parenthesis, mg, right parenthesis(mg) 1 quart left parenthesis, qt, right parenthesis(qt) = 2 pints left parenthesis, pt, right parenthesis(pt)
1 kilogram left parenthesis, kg, right parenthesis(kg) = 1000 grams left parenthesis, g, right parenthesis(g) 1 gallon left parenthesis, gal, right parenthesis(gal) = 4 quarts left parenthesis, qt, right parenthesis(qt)
1 ounce left parenthesis, oz, right parenthesis(oz) = 28.35 grams left parenthesis, g, right parenthesis(g) 1 cubic foot left parenthesis, ft³, right parenthesis(ft³) = 7.481 gallons left parenthesis, gal, right parenthesis(gal)
1 pound left parenthesis, lb, right parenthesis(lb) = 0.454 kilograms left parenthesis, kg, right parenthesis(kg) 1 liter left parenthesis, L, right parenthesis(L) = 1000 milliliters left parenthesis, mL, right parenthesis(mL)
1 cubic meter left parenthesis, m³, right parenthesis(m³) = 1000 liters left parenthesis, L, right parenthesis(L)
1 gallon left parenthesis, gal, right parenthesis(gal) = 3.785 liters left parenthesis, L, right parenthesis(L)
1 fluid ounce left parenthesis, fl oz, right parenthesis(fl oz) = 29.574 milliliters left parenthesis, mL, right parenthesis(mL)
*Note: you must use these exact conversion factors to get this question right.
Weight / mass Volume
1 pound left parenthesis, lb, right parenthesis(lb) = 16 ounces left parenthesis, oz, right parenthesis(oz) 1 cup left parenthesis, cup, right parenthesis(cup) = 8 fluid ounces left parenthesis, fl oz, right parenthesis(fl oz)
1 ton left parenthesis, ton, right parenthesis(ton) = 2000 pounds left parenthesis, lb, right parenthesis(lb) 1 pint left parenthesis, pt, right parenthesis(pt) = 2 cups left parenthesis, cups, right parenthesis(cups)
1 gram left parenthesis, g, right parenthesis(g) = 1000 milligrams left parenthesis, mg, right parenthesis(mg) 1 quart left parenthesis, qt, right parenthesis(qt) = 2 pints left parenthesis, pt, right parenthesis(pt)
1 kilogram left parenthesis, kg, right parenthesis(kg) = 1000 grams left parenthesis, g, right parenthesis(g) 1 gallon left parenthesis, gal, right parenthesis(gal) = 4 quarts left parenthesis, qt, right parenthesis(qt)
1 ounce left parenthesis, oz, right parenthesis(oz) = 28.35 grams left parenthesis, g, right parenthesis(g) 1 cubic foot left parenthesis, ft³, right parenthesis(ft³) = 7.481 gallons left parenthesis, gal, right parenthesis(gal)
1 pound left parenthesis, lb, right parenthesis(lb) = 0.454 kilograms left parenthesis, kg, right parenthesis(kg) 1 liter left parenthesis, L, right parenthesis(L) = 1000 milliliters left parenthesis, mL, right parenthesis(mL)
1 cubic meter left parenthesis, m³, right parenthesis(m³) = 1000 liters left parenthesis, L, right parenthesis(L)
1 gallon left parenthesis, gal, right parenthesis(gal) = 3.785 liters left parenthesis, L, right parenthesis(L)
1 fluid ounce left parenthesis, fl oz, right parenthesis(fl oz) = 29.574 milliliters left parenthesis, mL, right parenthesis(mL)
Answers
Answered by
GPT-4o mini
To find the density of the material expressed in ounces per cubic foot, we follow these steps:
1. **Convert the weight from kilograms to ounces**:
- The weight is given as 9 kilograms.
- Using the conversion factor:
\[
1 \text{ kg} = 0.454 \text{ lb}
\]
\[
9 \text{ kg} = 9 \times 0.454 \text{ lb} = 4.086 \text{ lb}
\]
- Now, convert pounds to ounces:
\[
1 \text{ lb} = 16 \text{ oz}
\]
\[
4.086 \text{ lb} = 4.086 \times 16 \text{ oz} = 65.376 \text{ oz}
\]
2. **Convert the volume from quarts to cubic feet**:
- The volume is given as 10 quarts.
- Using the conversion:
\[
1 \text{ qt} = \frac{1}{4} \text{ gal} \quad (\text{as } 1 \text{ gal} = 4 \text{ qt})
\]
\[
10 \text{ qt} = 10 \times \frac{1}{4} \text{ gal} = 2.5 \text{ gal}
\]
- Now convert gallons to cubic feet using the conversion factor:
\[
1 \text{ gal} = \frac{1}{7.481} \text{ ft}^3
\]
\[
2.5 \text{ gal} = 2.5 \times \frac{1}{7.481} \text{ ft}^3 \approx 0.3346 \text{ ft}^3
\]
3. **Calculate the density in ounces per cubic foot**:
- The density \(\rho\) is given by weight divided by volume:
\[
\rho = \frac{\text{weight (in ounces)}}{\text{volume (in cubic feet)}}
\]
\[
\rho = \frac{65.376 \text{ oz}}{0.3346 \text{ ft}^3} \approx 195.5 \text{ oz/ft}^3
\]
4. **Round to the nearest whole number**:
- Rounding \(195.5\) gives us \(196\).
The final density of the material is approximately **196 ounces per cubic foot**.
1. **Convert the weight from kilograms to ounces**:
- The weight is given as 9 kilograms.
- Using the conversion factor:
\[
1 \text{ kg} = 0.454 \text{ lb}
\]
\[
9 \text{ kg} = 9 \times 0.454 \text{ lb} = 4.086 \text{ lb}
\]
- Now, convert pounds to ounces:
\[
1 \text{ lb} = 16 \text{ oz}
\]
\[
4.086 \text{ lb} = 4.086 \times 16 \text{ oz} = 65.376 \text{ oz}
\]
2. **Convert the volume from quarts to cubic feet**:
- The volume is given as 10 quarts.
- Using the conversion:
\[
1 \text{ qt} = \frac{1}{4} \text{ gal} \quad (\text{as } 1 \text{ gal} = 4 \text{ qt})
\]
\[
10 \text{ qt} = 10 \times \frac{1}{4} \text{ gal} = 2.5 \text{ gal}
\]
- Now convert gallons to cubic feet using the conversion factor:
\[
1 \text{ gal} = \frac{1}{7.481} \text{ ft}^3
\]
\[
2.5 \text{ gal} = 2.5 \times \frac{1}{7.481} \text{ ft}^3 \approx 0.3346 \text{ ft}^3
\]
3. **Calculate the density in ounces per cubic foot**:
- The density \(\rho\) is given by weight divided by volume:
\[
\rho = \frac{\text{weight (in ounces)}}{\text{volume (in cubic feet)}}
\]
\[
\rho = \frac{65.376 \text{ oz}}{0.3346 \text{ ft}^3} \approx 195.5 \text{ oz/ft}^3
\]
4. **Round to the nearest whole number**:
- Rounding \(195.5\) gives us \(196\).
The final density of the material is approximately **196 ounces per cubic foot**.