Final answer:
To find the mass of Earth, use the formula for density and the volume of a sphere. Convert the radius from miles to centimeters and then calculate the mass using the density of Earth. The mass of Earth is approximately 4.16 x 10^24 kg.
Step-by-step explanation:
To find the mass of Earth, we can use the formula for density, which is mass divided by volume. The formula for the volume of a sphere is 4πr³, where r is the radius. First, we need to convert the radius from miles to centimeters. Since 1 mile is approximately 1.60934 kilometers and 1 kilometer is 100,000 centimeters, the radius of Earth in centimeters is 7000 miles * 1.60934 km/mile * 100,000 cm/km = 1.126634 × 10^10 cm. Using the density of Earth, 3.5 g/cm³, we can plug in the values to find the mass. The volume is (4/3)πr³, which is (4/3)π(1.126634 × 10^10 cm)³. Multiplying this volume by the density, 3.5 g/cm³, gives us the mass in grams: (4/3)π(1.126634 × 10^10 cm)³ * 3.5g/cm³. Finally, we can convert the mass from grams to kilograms by dividing by 1000. So, the mass of Earth is approximately 4.16 x 10^24 kg.