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.

Correct result:

V1-V2 =  512.6 mm3

Solution:

S1−S2=6a12−6a22=6((2r)2−(2r)2)=12r2=257 r=25712≐5 mm  V1−V2=a13−a23=(2r)3−(2r)3=512.6 mm3

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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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