Question

The volume of the oceans on Earth is approximately 1,386 million km^3. As the Earth's temperature rises, the ice in the polar icecaps melts into the oceans, increasing the volume of the oceans. If 1 cm^3 of ice melts, it turns into approximately 0.92 cm^3 water.

1) There are approximately 3,800 cm^3 in a gallon. If 1.9 m^3 of ice melts, how many gallons of water does this produce? (Round your answer to the nearest gallon.)

2) Scientists estimated that the addition of 1,000 km^3 of water would increase sea levels by 364 cm. Greenland's ice sheet is especially vulnerable to melting. Recent reports indicate a melting average of 195 km^3 of ice per year from Greenland, resulting in additional yearly 179.4 km^3 of water. If melting continues at this rate, how many centimeters would the sea increase after 6 years? (Round your answer to the nearest centimeter.)

Answer 1

1. 460 gallons
2. 392 cm

Explanation:

The necessary units conversion can be accomplished by multiplying by appropriate conversion factors. Quantity can be found by multiplying rate by time.

1)

The number of gallons of water produced by melting 1.9 m³ of ice is ...

`1.9\text{ m$^3$ (ice)}*\left(\frac{100\text{ cm}}{1\text{ m}}\right)^3*\frac{0.92\text{ cm$^3$ (water)}}{1\text{ cm$^3$ (ice)}}*\frac{1\text{ gal}}{3800\text{ cm$^3$}}\\\\=(1.9*10^6*0.92)/(3800)\text{ gal}=\boxed{460\text{ gal}}`

2)

Multiplying the melting rate by time and converting to height, we have ...

`\frac{179.4\text{ km$^3$}}{1\text{ yr}}*\frac{364\text{ cm}}{1000\text{ km$^3$}}*6\text{ yr}\approx\boxed{392\text{ cm}}`

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Additional comment

The area of the world's oceans is about 361e6 km², so addition of 1000 km³ of water might be expected to increase the water level by (1000/361)e-6 ≈ 2.77e-6 km = 0.277 cm. Something seems a little off in this problem statement.