Cube in a sphere

The cube is inscribed in a sphere with volume 9067 cm3. Determine the length of the edges of a cube.

Result

a =  14.9 cm

Solution:

V=9067 cm3 V=43πr3  r=3⋅ V4π3=3⋅ 90674⋅ 3.14163≐12.9358 cm  D=2⋅ r=2⋅ 12.9358≐25.8715 cm  u=D=25.8715≐25.8715 cm  u=3a  a=u/3=25.8715/3≐14.9369=14.9  cm V = 9067 \ cm^3 \ \\ V = \dfrac{ 4 }{ 3 } \pi r^3 \ \\ \ \\ r = \sqrt[3]{ \dfrac{ 3 \cdot \ V }{ 4 \pi } } = \sqrt[3]{ \dfrac{ 3 \cdot \ 9067 }{ 4 \cdot \ 3.1416 } } \doteq 12.9358 \ cm \ \\ \ \\ D = 2 \cdot \ r = 2 \cdot \ 12.9358 \doteq 25.8715 \ cm \ \\ \ \\ u = D = 25.8715 \doteq 25.8715 \ cm \ \\ \ \\ u = \sqrt{ 3 } a \ \\ \ \\ a = u/\sqrt{ 3 } = 25.8715/\sqrt{ 3 } \doteq 14.9369 = 14.9 \ \text { cm }

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i am good at this

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