Question

Clouds can weigh thousands of pounds due to their liquid water content. Often this content is measured in grams per cubic meter (g/m3). Assume that a cumulus cloud occupies a volume of one cubic kilometer, and its liquid water content is 0.2 g/m3. (a) What is the volume of this cloud in cubic miles? (b) How much does the water in the cloud weigh in pounds?

Answer 1

The volume of a cumulus cloud occupying one cubic kilometer is equal to 0.386102 cubic miles. The water inside this cloud, with a liquid water content of 0.2 g/m³, weighs approximately 441 pounds.

Step-by-step explanation:

The subject of this problem is to find the volume of a cloud in a different unit of measure and the weight of the water within it. Volume conversion from cubic kilometers to cubic miles and weight calculation of water in pounds are required.

To find the volume of the cloud in cubic miles, we use the conversion factor that 1 cubic kilometer is equal to about 0.386102 cubic miles. Hence, the volume of 1 cubic kilometer in cubic miles is:

1 cubic kilometer * 0.386102 cubic miles/cubic kilometer = 0.386102 cubic miles.

Next, we calculate the weight of the water in pounds, considering that the liquid water content is 0.2 grams per cubic meter and there are 1,000,000 cubic meters in a cubic kilometer:

0.2 g/m³ * 1,000,000 m³/km³ = 200,000 grams of water in the cloud.

Now, convert grams to pounds using the conversion factor 453.59237 grams per pound:

200,000 grams * (1 pound / 453.59237 grams) = 441 pounds.

Therefore, the water weight in the cloud is 441 pounds.

Answer 2

a) 0.2399 mi³

b) 440.8 × 10³ Pounds

Step-by-step explanation:

Given:

Volume of cumulus cloud, V = 1 km³

Liquid water content = 0.2 g/m³

Now,

a) 1 km =
`\frac{\textup{1 miles}}{\textup{1.6093}}`

thus,

1 km³ =
`(\frac{\textup{1 miles}}{\textup{1.6093}})^3`

1 km³ = 0.2399 mi³

Hence, volume of cloud in cubic miles is 0.2399 mi³

b)

Liquid water content = 0.2 g/m³

Now,

1 Km = 1000 m

thus,

1 km³ = 1000³ m³

Therefore,

Liquid water content in 1 Km³ of cloud = 0.2 g/m³ × 1000³ m³

= 200 × 10⁶ gram

or

= 200 × 10³ Kg

also,

1 kilogram = 2.204 pounds

Therefore,

200 × 10³ Kg = 200 × 10³ × 2.204 pounds = 440.8 × 10³ Pounds