The radius of the Earth is approximately 3,960 miles. Find the approximate surface-area-to-volume ratio of the Earth.
To find the surface-area-to-volume ratio of the Earth, we need to determine the surface area and volume of the Earth.
1. Surface Area of a Sphere:
The surface area of a sphere can be calculated using the formula:
Surface Area = 4πr^2, where "π" is approximately 3.14159 and "r" is the radius.
Since the radius of the Earth is given as 3,960 miles, we can substitute this value into the formula to calculate the surface area.
Surface Area = 4π(3960)^2
2. Volume of a Sphere:
The volume of a sphere can be calculated using the formula:
Volume = (4/3)πr^3
Again, we substitute the radius into the formula to calculate the volume.
Volume = (4/3)π(3960)^3
3. Now, we can calculate the surface-area-to-volume ratio by dividing the surface area by the volume:
Surface-area-to-volume ratio = Surface Area / Volume
Substituting the values we calculated for surface area and volume, we get:
Surface-area-to-volume ratio = (4π(3960)^2) / [(4/3)π(3960)^3]
Simplifying the equation:
Surface-area-to-volume ratio = 3(3960)^2 / 3(3960)^3
Since 3 is common in both the numerator and denominator, they cancel out:
Surface-area-to-volume ratio = (3960)^2 / (3960)^3
Calculating this expression:
Surface-area-to-volume ratio ≈ 0.238
Therefore, the approximate surface-area-to-volume ratio of the Earth is approximately 0.238.
A=4πr^2
V=4/3πr^3
A/V = 4πr^2/(4/3πr^3)
Some of the terms cancel each other out.
4πr^2/(4/3πr^3) = 1/3r