Question

Estimate the mass of water on the earth. The density of water is 1000kg per cubic meter. Give the answer to 1 significant figure. There are some approximations that can be used: compared with the oceans, lakes and rivers are tiny. Clouds have very low density. There is (still) lots of ice in the polar regions, but much less area which covers roughly 2/3 of the earth. Looking at the charts of the oceans, we see that the depth is typically several thousand meters (and a serious search tells me the average depth is 4700m). The radius of the earth is about 6000km. The surface area of a sphere is 4R².

a. 1* 10^21 kg
b. 2 * 10^21 kg
c. 3*10^21 kg
d. 4 *10^21 kg

Answer 1

To estimate the mass of water on Earth, the Earth's surface area is calculated using its radius, then multiplied by the average depth of the oceans to get the volume, which is then multiplied by the density of water to find the mass, resulting in approximately 7 x 10²ⁱ kg.

Step-by-step explanation:

To estimate the mass of water on Earth, we will use the provided parameters such as the density of water, the average depth of the oceans, and the radius of the Earth. The density of water is given as 1000 kg per cubic meter. Considering that about 2/3 of Earth's surface is covered with water and the average depth of oceans is 4700 meters, we can estimate the surface area of the oceans.

First, we estimate the Earth's surface area using the formula A = 4πR², where R is the radius of the Earth (approximately 6,000,000 meters). Thus, the surface area of Earth is A ≈ 4π(6 × 10⁶ m)² ≈ 4π(36 × 10¹⁲ m²) ≈ 4 × 3.14 × 36 × 10¹⁲ m² ≈ 1.5 × 10ⁱ⁵ m².

Next, we multiply the Earth's surface area by the average ocean depth to find the volume of the oceans, V = A × D which gives us V ≈ 1.5 × 10ⁱ⁵ m² × 4700 m ≈ 7.05 × 10¹⁸ m³.

Lastly, we calculate the mass by multiplying the volume by the density of water: mass = density × volume ≈ 1000 kg/m³ × 7.05 × 10¹⁸ m³ ≈ 7.05 × 10²ⁱ kg.

This result should be expressed with one significant figure: 7 × 10²ⁱ kg, which closely aligns to choice (a) 1 × 10²ⁱ kg.