10. About \( 29 \% \) of Earth's surface is land; the rest is water. The radius of is about 2,100 miles, while the radius of Earth is about 3,960 miles. But virtually all of the surface of Mars is land. To the nearest percent, what is the ratio of the surface area of Mars to the land area of Earth?

To find the ratio of the surface area of Mars to the land area of Earth, we first need to calculate the surface areas of both. The formula for the surface area of a sphere is given by: \[ \text{Surface Area} = 4\pi r^2 \] Calculating the surface area of Mars: - The radius of Mars is approximately 2,100 miles. \[ \text{Surface Area of Mars} = 4\pi (2100^2) \approx 4\pi (4,410,000) \approx 55,292,120 \text{ square miles} \] Now, calculating the surface area of Earth: - The radius of Earth is approximately 3,960 miles. \[ \text{Surface Area of Earth} = 4\pi (3960^2) \approx 4\pi (15,681,600) \approx 197,465,600 \text{ square miles} \] Next, we find the land area of Earth. Since about \( 29\% \) of Earth's surface is land: \[ \text{Land Area of Earth} = 0.29 \times 197,465,600 \approx 57,314,224 \text{ square miles} \] Finally, we need to calculate the ratio of the surface area of Mars to the land area of Earth: \[ \text{Ratio} = \frac{\text{Surface Area of Mars}}{\text{Land Area of Earth}} \approx \frac{55,292,120}{57,314,224} \approx 0.964 \] Converting this ratio to a percentage gives: \[ 0.964 \times 100 \approx 96.4\% \text{ (approximately 96\% when rounded to the nearest percent)} \] Thus, the ratio of the surface area of Mars to the land area of Earth to the nearest percent is approximately \( 96\% \).