Hi,

.



app 255.5 cm^3 space is in between 

Answer by CharlesG2(834)   (Show Source): You can put this solution on YOUR website!
 The two spheres above have the same center. One has a radius of 4 cm, and the other has a radius of 5 cm. Approximately how much space is in between the two spheres



sphere A radius 4 cm so r[A] = 4 cm

sphere B radius 5 cm so r[B] = 5 cm



distance between the surfaces of the 2 spheres is 1 cm



to find volume of each sphere and the difference in volume:



V[sphere] = 4/3 * pi * radius ^ 3



V[B - A] = V[B] - V[A]

V[B - A] = 4/3 * pi * 5 ^ 3 - 4/3 * pi * 4 ^ 3

V[B - A] = 4/3 * pi * (5^3 - 4^3) or 4/3 * pi * ( r[B] - r[A] ) (factored)



V[B] = 4/3 * pi * 125 = (125 * 4)/3 * pi

V[A] = 4/3 * pi * 64 = (64 * 4)/3 * pi

difference is (61 * 4)/3 * pi



V[B - A] = 4/3 * pi * (125 - 64)

V[B - A] = 4/3 * pi * 61

V[B - A] = (61 * 4)/3 * pi

V[B - A] = 244/3 * pi cm^3



 

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