Given \( V = 100 \), we solve for \( s \):
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- A data storage device is modeled as a regular tetrahedron with side length \( s \). If the volume of the device is 100 cubic units, find the side length \( s \).
- The volume \( V \) of a regular tetrahedron with side length \( s \) is given by:
- V = \frac{s^3}{6\sqrt{2}}
- \frac{s^3}{6\sqrt{2}} = 100
- s^3 = 100 \times 6\sqrt{2} = 600\sqrt{2}
- s = \sqrt[3]{600\sqrt{2}}
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