Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.

Result

V1-V2 =  512.6 mm3

Solution:

S1S2=6a126a22=6((2r)2(2r)2)=12r2=257 r=257125 mm  V1V2=a13a23=(2r)3(2r)3=512.6 mm3S_1- S_2 = 6a_1^2-6a_2^2 = 6((2r)^2-(\sqrt2 r)^2) = 12 r^2 = 257 \ \\ r=\sqrt{ \dfrac{ 257}{12} } \doteq 5 \ mm \ \\ \ \\ V_1-V_2 = a_1^3-a_2^3 = (2r)^3-(\sqrt2 r)^3 = 512.6 \ \text{mm}^3



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Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

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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