the earth is approximately sphere of radius 6.37*10^6 meter.what is its surface area in square km? what is its volume in cubic km?
a = 4πr^2
v = 4/3 πr^3
plug and chug with r = 6370 km
To calculate the surface area of a sphere, we use the formula:
Surface Area = 4πr^2
Given that the radius of the Earth is 6.37 x 10^6 meters, we can substitute this value into the formula to calculate the surface area.
Surface Area = 4π(6.37 x 10^6)^2
To find the volume of a sphere, we use the formula:
Volume = (4/3)πr^3
Substituting the radius of the Earth into the formula, we can calculate the volume.
Volume = (4/3)π(6.37 x 10^6)^3
Now, let's calculate the values using a calculator.
Calculating surface area:
Surface Area = 4π(6.37 x 10^6)^2
≈ 4 x 3.14 x (6.37 x 10^6)^2
≈ 4 x 3.14 x 40.5769 x 10^12
≈ 515.3 x 10^12 square meters
To convert it to square kilometers, we divide by 1,000,000 (since 1 square kilometer = 1,000,000 square meters):
Surface Area ≈ 515.3 x 10^12 / 1,000,000
≈ 515.3 x 10^6 square kilometers
Therefore, the surface area of the Earth is approximately 515.3 million square kilometers.
Calculating volume:
Volume = (4/3)π(6.37 x 10^6)^3
≈ (4/3) x 3.14 x (6.37 x 10^6)^3
≈ 4.19 x (259.0 x 10^18)
≈ 1082.6 x 10^18 cubic meters
To convert it to cubic kilometers, we divide by 1,000,000,000,000 (since 1 cubic kilometer = 1,000,000,000,000 cubic meters):
Volume ≈ 1082.6 x 10^18 / 1,000,000,000,000
≈ 1.0826 x 10^12 cubic kilometers
Therefore, the volume of the Earth is approximately 1.0826 trillion cubic kilometers.