Cubes

One cube is an inscribed sphere, and the other one is 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 = S1  S2 S1 = 4 π r12 S2 = 4 π r22  2r1 = 3 a 2r2 = a  S = 3 π a2  π a2 = 2 π a2 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=26932231=2693231=2462=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?

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





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