The radius of the Earth is approximately 3,960 miles. Find the approximate surface-area-to-volume ratio of the Earth.
A.
0.00025
B.
0.00076
C.
1,320
D.
11,880
4πR²3/(4πR³) = 3/R = 3/3960=0.00076
If a sphere’s volume is doubled, what is the corresponding change in its radius?
To find the surface-area-to-volume ratio of the Earth, you need to find the surface area and volume of the Earth using the given radius.
1. Surface area of a sphere: The formula for the surface area of a sphere is given by 4πr^2, where r is the radius.
Calculate the surface area using the given radius:
Surface area = 4π(3960)^2
≈ 4π(15,681,600)
≈ 62,726,400π
2. Volume of a sphere: The formula for the volume of a sphere is given by (4/3)πr^3, where r is the radius.
Calculate the volume using the given radius:
Volume = (4/3)π(3960)^3
≈ (4/3)π(62,523,360,000)
≈ 83,364,480,000π
3. Surface-area-to-volume ratio: Divide the surface area by the volume to get the ratio.
Surface-area-to-volume ratio = Surface area / Volume
= (62,726,400π) / (83,364,480,000π)
≈ 0.00075
Therefore, the approximate surface-area-to-volume ratio of the Earth is approximately 0.00076.
Hence, the correct answer is option B.
To find the approximate surface-area-to-volume ratio of the Earth, we need to calculate the surface area and the volume of the Earth.
The surface area of a sphere can be calculated using the formula: 4πr^2, where r is the radius.
In this case, the radius of the Earth is given as approximately 3,960 miles. Plugging this value into the formula, we can calculate the surface area.
Surface Area = 4π(3960)^2
Using a calculator, we get the surface area to be approximately 197,352,335 square miles.
The volume of a sphere can be calculated using the formula: (4/3)πr^3.
Plugging in the given radius, we can calculate the volume:
Volume = (4/3)π(3960)^3
Using a calculator, we get the volume to be approximately 260,519,953,474 cubic miles.
Now, to find the surface-area-to-volume ratio, we divide the surface area by the volume:
Surface-area-to-volume ratio = Surface Area / Volume
Surface-area-to-volume ratio = 197,352,335 / 260,519,953,474
Calculating this ratio using a calculator, we get the value to be approximately 0.00076.
Therefore, the correct answer is B. 0.00076.