The relationship between the radius of a sphere and its surface area is given by: \[ \mathrm{SA}=4 \pi^{2} \] where \( S A= \) surface area and \( r= \) radius. 1st attempt Part 1 ( 0.5 point) See Periodic Table The mean radius of the Earth is \( 6,371 \mathrm{~km} \), and \( 70.8 \% \) of its surface is covered by water. What is the surface area of the Earth covered by land? \( \square \) \( \mathrm{km}^{2} \)

To find the surface area of the Earth covered by land, we first need to calculate the total surface area of the Earth using the formula \( SA = 4\pi r^2 \). Given that the mean radius \( r \) is \( 6,371 \) km, we can substitute this value into the equation: \[ SA = 4\pi (6,371^2) \approx 510,072,000 \text{ km}^2. \] Next, since \( 70.8\% \) of the Earth's surface is covered by water, we can calculate the area covered by water: \[ \text{Area covered by water} = 0.708 \times 510,072,000 \approx 361,132,160 \text{ km}^2. \] Now, we subtract this from the total surface area to find the land area: \[ \text{Area covered by land} = 510,072,000 - 361,132,160 \approx 148,939,840 \text{ km}^2. \] Thus, the surface area of the Earth covered by land is \( 148,939,840 \text{ km}^2 \). The formula for calculating the surface area of a sphere may seem abstract, but its roots can be traced back to ancient mathematicians like Archimedes. He derived many geometrical concepts that are foundational to our understanding of volume and surface areas today! In real-world applications, understanding the relationship between the radius and surface area of a sphere helps in fields like environmental science, where estimating areas of oceans vs. land is crucial for climate models, conservation efforts, and urban planning. For instance, when assessing the land available for agriculture or human habitation, knowledge of surface area can inform sustainable practices while preserving natural landscapes.