# 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:

$S_1- S_2 = 6a_1^2-6a_2^2 = 6((2r)^2-(\sqrt2 r)^2) = 12 r^2 = 257 \ \\ r=\sqrt{ \dfrac{ 257}{12} } \doteq 5 \ mm \ \\ \ \\ V_1-V_2 = a_1^3-a_2^3 = (2r)^3-(\sqrt2 r)^3 = 512.6 \ \text{mm}^3$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors. 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) Tips to related online calculators
Tip: Our volume units converter will help you with the conversion of volume units.
Pythagorean theorem is the base for the right triangle calculator.

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