SOLUTION: (This is pre cal 11- chapter 2: absolute value and radicals) Earth approximates a sphere with radius 6370km. a) The formula for the surface area of a sphere is : SA= 4πrē

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Question 764974: (This is pre cal 11- chapter 2: absolute value and radicals)
Earth approximates a sphere with radius 6370km.
a) The formula for the surface area of a sphere is : SA= 4πrē
To the nearest kilometer, determine the edge length of a cube with the same surface area as Earth.
b) The formula for the volume of a sphere is: V=4/3πrē
To the nearest kilometer, determine the edge length of a cube with the same volume as Earth.
Thank you.
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Earth approximates a sphere with radius 6370km.
a) The formula for the surface area of a sphere is : SA= 4πrē
SA = 4pi*6370^2
--------------------------
To the nearest kilometer, determine the edge length of a cube with the same surface area as Earth.
sa for a cube is 6e^2 where e is the edge length.
Solve 6e^2 = 4pi*6370^2
cube edge = sqrt[4pi*6370^2/6] = 6370*sqrt(2pi/3)

b) The formula for the volume of a sphere is: V=4/3πrē
V = (4/3)pi(6370)^3
To the nearest kilometer, determine the edge length of a cube with the same volume as Earth.
cube volume = e^3
-----
Solve e^3 = (4/3)pi(6370)^3
---
cube edge = 6370*cbrt(4pi/3)
================================
Cheers,
Stan H.
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