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The edge length, s, of a regular tetrahedron is approximately given by , where V is the volume of the terahedron. Use a graphing calculator to graph the function. Estimate the volume of a regular tetrhedron with an edge length of 4 inches.

Respuesta :

Volume of a tetrahedron with edge s

[tex]\\ \rm\Rrightarrow V=\dfrac{s^3}{6\sqrt{2}}[/tex]

According to question

  • s=4in

[tex]\\ \rm\Rrightarrow V=\dfrac{4^3}{6\sqrt{2}}[/tex]

[tex]\\ \rm\Rrightarrow V=\dfrac{64}{6\sqrt{2}}[/tex]

[tex]\\ \rm\Rrightarrow V=\dfrac{32}{3\sqrt{2}}[/tex]

[tex]\\ \rm\Rrightarrow V=\dfrac{32}{4.2426406871192}[/tex]

[tex]\\ \rm\Rrightarrow V\approx 7.5425in^3[/tex]

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Answer:

See below ~

Step-by-step explanation:

Volume of a tetrahedon

  • V = s³ / 6√2
  1. s = edge length

Solving for V

  • V = (4)³ / 6√2
  • V = 64 / 6√2
  • V = 32 / 3√2
  • V = 32√2 / 6
  • V = 16√2 / 3
  • V = 7.54 cubic inches

Graph

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