Earth can be modeled by a sphere with a diameter of 7,918 miles. Given that 29% of Earth’s surface is land, which of the following is closest to the total area, in square miles, of land on Earth?Responses5.7×107Answer A: 5.7 times 10 to the seventh powerA2.3×108Answer B: 2.3 times 10 to the eighth powerB7.5×1010Answer C: 7.5 times 10 to the tenth powerC

To find the total area of land on Earth, we need to follow these steps:

1. Calculate the surface area of Earth using the formula for the surface area of a sphere: $\text{Surface Area} = 4 \pi r^2$ where $r$ is the radius of the sphere.

2. Given the diameter of Earth is 7,918 miles, the radius $r$ is half of the diameter: $r = \frac{7,918}{2} = 3,959 \text{ miles}$

3. Substitute the radius into the surface area formula: $\text{Surface Area} = 4 \pi (3,959)^2$

4. Calculate $(3,959)^2$: $(3,959)^2 \approx 15,678,481$

5. Multiply by $4 \pi$: $4 \pi \times 15,678,481 \approx 196,935,000 \text{ square miles}$

6. Given that 29% of Earth’s surface is land, calculate the land area: $\text{Land Area} = 0.29 \times 196,935,000 \approx 57,111,150 \text{ square miles}$

7. Express the result in scientific notation: $57,111,150 \approx 5.7 \times 10^7$

Therefore, the closest total area of land on Earth is: $\boxed{5.7 \times 10^7}$