Assuming that 68.1% of the Earth's surface is covered with water at average depth of 1.21 mi. ,estimate the mass of the water on Earth. One mile is 1.609 km and the radius
of the earth is 6.37 x 10^6 m. Answer in units of kg
The volume in cubic meters is the product of the ocean area (in m^2) and the average depth (in meters).
For the ocean area, take 68.1% of 4*pi*R^2.
For the mass of the water, multiply the volume by 1000 kg/m^3. Actually you should use a higher density of 1027 kg/m^3, corresponding to ocean salt water, since that is what most of it is.
Calculating these numbers yourself will improve your learning experience
I multiplied 68.1 X 5.099043638x10^14=3.472448717x10^16 to get the ocean area.
Then to get the average depth i took 1.21mix1609m=1946.89.
Then i multiplied the ocean area and volume i got to equal 6.760475683x10^19.
To get the mass, I took that answer and multiplied it to 1000 kg/m^3. I got 6.760475683x10^22. If i put that in significant figures it woud just be 6.76 x 10^22 kg right? was my method correct?
To estimate the mass of the water on Earth, we need to calculate the volume of water and then multiply it by the density of water. Here are the steps to follow:
Step 1: Calculate the radius of the Earth in kilometers.
The radius of the Earth is given as 6.37 × 10^6 m. To convert it to kilometers, multiply it by 0.001:
Radius = 6.37 × 10^6 m × 0.001 = 6.37 × 10^3 km
Step 2: Calculate the surface area of the Earth covered with water.
We're given that 68.1% of the Earth's surface is covered with water. To find the surface area, we can multiply the total surface area of the Earth by the percentage:
Surface area of Earth = 4π × radius^2
Surface area of water = 68.1% × Surface area of Earth
Step 3: Calculate the volume of water.
The volume of water can be found by multiplying the surface area of water by the average depth:
Volume of water = Surface area of water × Average depth in kilometers
Step 4: Multiply the volume of water by the density of water.
The density of water is approximately 1000 kg/m^3. To convert the volume from km^3 to m^3, multiply it by 1,000,000,000:
Mass of water = Volume of water (in m^3) × Density of water
Step 5: Convert the mass of water to kilograms.
The units for the mass of water will be in kg, so we don't need to make any further conversions.
Let's calculate the mass of the water on Earth using these steps:
Step 1: Radius = 6.37 × 10^3 km
Step 2: Surface area of water = 68.1% × (4π × radius^2)
Step 3: Volume of water = Surface area of water × 1.21 km
Step 4: Mass of water = Volume of water (in m^3) × 1,000,000,000 × Density of water
Step 5: Express the mass of water in kg.
By following these steps, we can estimate the mass of the water on Earth.