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Physicsrapper
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10 000 cubic km of water can cover all the continents with a layer 7 cm deep.
Find the depth of the water layer if 10 000 cubic km of water is spread over a sphere with radius R = 6370 km.
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My calculations:
Volume of the sphere: 4/3*π*r^3
R* = R + d (d = depht of the water=> searched)
d = R* - R
V* = V + v (V = 4/3*π*6370^3 ; is the little v equal to the 10 000 km^3?)
Would that be correct:
V = 4/3*π*6370^3 = 1.0826969e+12 km^3 (?)
v = 10 000 km^3 (?)
Total V*: 1.0826969e+12
Next we search R*:
Volume of the sphere: V* = 4/3*π*R*^3
=> R*^3 = V*/π*3/4
= (1.0826969e+12/π)*3/4 => take the third root = 1.73205080757
So d ~ 1.73 cm ?
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Please correct this! I'm really not sure if it's correct.
Can someone please help and explain what I did wrong?
Find the depth of the water layer if 10 000 cubic km of water is spread over a sphere with radius R = 6370 km.
________________________________________________
My calculations:
Volume of the sphere: 4/3*π*r^3
R* = R + d (d = depht of the water=> searched)
d = R* - R
V* = V + v (V = 4/3*π*6370^3 ; is the little v equal to the 10 000 km^3?)
Would that be correct:
V = 4/3*π*6370^3 = 1.0826969e+12 km^3 (?)
v = 10 000 km^3 (?)
Total V*: 1.0826969e+12
Next we search R*:
Volume of the sphere: V* = 4/3*π*R*^3
=> R*^3 = V*/π*3/4
= (1.0826969e+12/π)*3/4 => take the third root = 1.73205080757
So d ~ 1.73 cm ?
______________________________________
Please correct this! I'm really not sure if it's correct.
Can someone please help and explain what I did wrong?