One cube is an inscribed sphere and the other one described. Calculate the difference of volumes of cubes, if the difference of surfaces in 231 cm2.

Correct answer:

x =  489.8 cm3

Step-by-step explanation:

S=231 cm2 S=S1S2 S1=4 πr12 S2=4 πr22  2r1=3a 2r2=a  S=3 πa2πa2=2 πa2 a=2πS=2 3.14162316.0634 cm r2=a/2=6.0634/23.0317 cm r1=3 r2=3 3.03175.2511 cm  V1=34 π r13=34 3.1416 5.25113606.497 cm3 V2=34 π r23=34 3.1416 3.03173116.7204 cm3  x=V1V2=606.497116.7204489.7766 cm3  Verifying Solution:  S1=4π r12=4 3.1416 5.25112=2693=346.5 cm2 S2=4π r22=4 3.1416 3.03172=2231=115.5 cm2 ΔS=S1S2=346.5115.5=231 cm2

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Showing 2 comments:
Math student
What do all those symbols mean? Is there a more simple format...that you could put this in?

S - surface area of cube
V - volume of cube(s)
r - radius of sphere

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