Question
The density of a certain material is such that it weighs 6200 ounces per cubic foot of volume. Express this density in tons per cubic meter. Round your answer to the nearest hundredth.
*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 convert the density from ounces per cubic foot to tons per cubic meter, we can follow these steps:
1. **Convert ounces to pounds**:
\[
1 \text{ lb} = 16 \text{ oz} \implies 6200 \text{ oz} = \frac{6200}{16} \text{ lb}
\]
\[
6200 \text{ oz} = 387.5 \text{ lb}
\]
2. **Convert pounds to tons**:
\[
1 \text{ ton} = 2000 \text{ lb} \implies 387.5 \text{ lb} = \frac{387.5}{2000} \text{ ton}
\]
\[
387.5 \text{ lb} = 0.19375 \text{ ton}
\]
3. **Convert cubic feet to cubic meters**:
\[
1 \text{ ft}^3 = 7.481 \text{ gal} \implies 1 \text{ gal} = 3.785 \text{ L} \implies 1 \text{ ft}^3 = 7.481 \times 3.785 \text{ L}
\]
First, we calculate how many liters are in a cubic foot:
\[
7.481 \text{ gal} \times 3.785 \text{ L/gal} = 28.316846 \text{ L}
\]
Note that \(1 \text{ L} = 0.001 \text{ m}^3\):
\[
1 \text{ ft}^3 = 28.316846 \text{ L} \implies 1 \text{ ft}^3 = 0.028316846 \text{ m}^3
\]
4. **Calculate density in tons per cubic meter**:
Density in tons per cubic meter is:
\[
\text{Density} = \frac{0.19375 \text{ ton}}{0.028316846 \text{ m}^3}
\]
\[
\text{Density} = 6.84555 \text{ ton/m}^3
\]
5. **Round the result to the nearest hundredth**:
The final density rounded to the nearest hundredth is:
\[
\text{Density} \approx 6.85 \text{ tons/m}^3
\]
Thus, the density of the material expressed in tons per cubic meter is approximately **6.85 tons/m³**.
1. **Convert ounces to pounds**:
\[
1 \text{ lb} = 16 \text{ oz} \implies 6200 \text{ oz} = \frac{6200}{16} \text{ lb}
\]
\[
6200 \text{ oz} = 387.5 \text{ lb}
\]
2. **Convert pounds to tons**:
\[
1 \text{ ton} = 2000 \text{ lb} \implies 387.5 \text{ lb} = \frac{387.5}{2000} \text{ ton}
\]
\[
387.5 \text{ lb} = 0.19375 \text{ ton}
\]
3. **Convert cubic feet to cubic meters**:
\[
1 \text{ ft}^3 = 7.481 \text{ gal} \implies 1 \text{ gal} = 3.785 \text{ L} \implies 1 \text{ ft}^3 = 7.481 \times 3.785 \text{ L}
\]
First, we calculate how many liters are in a cubic foot:
\[
7.481 \text{ gal} \times 3.785 \text{ L/gal} = 28.316846 \text{ L}
\]
Note that \(1 \text{ L} = 0.001 \text{ m}^3\):
\[
1 \text{ ft}^3 = 28.316846 \text{ L} \implies 1 \text{ ft}^3 = 0.028316846 \text{ m}^3
\]
4. **Calculate density in tons per cubic meter**:
Density in tons per cubic meter is:
\[
\text{Density} = \frac{0.19375 \text{ ton}}{0.028316846 \text{ m}^3}
\]
\[
\text{Density} = 6.84555 \text{ ton/m}^3
\]
5. **Round the result to the nearest hundredth**:
The final density rounded to the nearest hundredth is:
\[
\text{Density} \approx 6.85 \text{ tons/m}^3
\]
Thus, the density of the material expressed in tons per cubic meter is approximately **6.85 tons/m³**.