In 2017, approximately 7.7 x 108 kg polyethylene terephthalate (PET) bottles were collected through recycling programs and sold, either to domestic or foreign markets. If the density of PET is 1350 kg/m3, the volume of PET that was recycled in 2017 was _________ m3.

Question

In 2017, approximately 7.7 x 108 kg polyethylene terephthalate (PET) bottles were collected through recycling programs and sold, either to domestic or foreign markets.  If the density of PET is 1350 kg/m3, the volume of PET that was recycled in 2017 was  _________ m3.

BlackTom AI · Accepted Answer

First, restate the problem in my own words to ensure understanding: we have a mass of PET equal to 7.7 x 10^8 kg, and the density of PET is 1350 kg/m^3. We need to find the corresponding volume in cubic meters.
Option-by-option analysis:
- Option 1: 1.75. This looks like a number without units and far too small for a volume in cubic meters given the mass; it does not align with the mass-to-volume relationship V = m / ρ, so this is unlikely to be correct.
- Option 2: 570,370. This value is on the order of hundreds of thousands of cubic meters, which matches the scale expected when converting a mass of hundreds of millions of kilograms by a density around a thousand kilograms per cubic meter. To check, compute V = m / ρ = (7.7 x 10^8 kg) / (1350 kg/m^3) ≈ 5.7037 x 10^5 m^3, which equals 570,370 m^3 when expressed as an integer. This matches the expected calculation result.
- Option 3: 1.0395 x 10^12. This is on the order of trillions of cubic meters, which is several orders of magnitude larger than the mass provided would yield with the given density. It would correspond to a mass around ρ x V ≈ 1.395 x 10^15 g, far exceeding 7.7 x 10^8 kg, so it's implausible here.
- Option 4: 770,001,350. This is about 7.7 x 10^8, but as a volume in m^3 it would imply an unusually large density or mass; numerically, it doesn’t align with V = m/ρ using ρ = 1350 kg/m^3, since m/ρ would give a much smaller value around 5.7 x 10^5 m^3, not hundreds of millions of m^3.
- Option 5: 770,000,000. Similar to Option 4, this is 7.7 x 10^8 m^3, which is far larger than the volume calculated from the given mass and density. This would imply a density or mass inconsistent with the provided data.
- Option 6: 570,370,000. This is 5.7037 x 10^8 m^3, which is about a thousand times larger than the expected volume from V = m/ρ for the given mass and density. It indicates a misplacement of the decimal point relative to the correct calculation.
- Option 7: 570. This is far too small by about six orders of magnitude, and would only be reasonable for a mass around ρ x V ≈ 1350 x 570 ≈ 769,500 kg, which is far below the given 7.7 x 10^8 kg. So this cannot be correct.
Putting the pieces together, only Option 2 yields a volume consistent with V = m/ρ when m = 7.7 x 10^8 kg and ρ = 1350 kg/m^3; the calculation m/ρ = (7.7 x 10^8) / 1350 ≈ 5.7037 x 10^5 m^3, i.e., 570,370 m^3. The other options either overestimate by orders of magnitude or underestimate by several orders, indicating they fail to satisfy the fundamental relation between mass, density, and volume.

In 2017, approximately 7.7 x 108 kg polyethylene terephthalate (PET) bottles were collected through recycling programs and sold, either to domestic or foreign markets. If the density of PET is 1350 kg/m3, the volume of PET that was recycled in 2017 was _________ m3.

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In 2017, approximately 7.7 x 108 kg polyethylene terephthalate (PET) bottles were collected through recycling programs and sold, either to domestic or foreign markets. If the density of PET is 1350 kg/m3, the volume of PET that was recycled in 2017 was _________ m3.

View Explanation

Log in for full answers

Similar Questions

​Because freshwater is denser than seawater, seawater floats on top of freshwater.

Question at position 3 The key property that determines whether fluid (air or water) sinks or rises is _________.densitycolorsound

The mass of a metal ball bearing is 0.3062 g and the volume is 0.0270 cm3. What is the density?

The density of gold is 19.32 g/cm3. What is the mass of a bar of gold measuring 4.50 cm by 2.50 cm by 6.50 cm?

Which one of the following substances will float in gasoline, which has a density of 0.66 g/mL?

2. A plastic container has a mass of 62 g and a volume of 44.3 cm3. a. What is the density of the plastic container in g/cm3?

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