Respuesta :
Slant height of tetrahedron is=6.53cm
Volume of the tetrahedron is=60.35[tex]\mathrm{cm}^{3}[/tex]
Given:
Length of each edge a=8cm
To find:
Slant height and volume of the tetrahedron
Step by Step Explanation:
Solution;
Formula for calculating slant height is given as
Slant height=[tex]\sqrt{\frac{2}{3}} a[/tex]
Where a= length of each edge
Slant height=[tex]\sqrt{\frac{2}{3}} \times 8[/tex]
=[tex]\sqrt{0.6667} \times 8[/tex]
=[tex]0.8165 \times 8[/tex]=6.53cm
Similarly formula used for calculating volume is given as
Volume of the tetrahedron=[tex]\frac{a^{3}}{6 \sqrt{2}}[/tex]
Substitute the value of a in above equation we get
Volume=[tex]\frac{8^{5}}{6 \sqrt{2}}[/tex]
=[tex]\frac{512}{6 \sqrt{2}}[/tex]
=[tex]\frac{512}{6 \times 1.414}[/tex]
Volume=[tex]512 / 8.484[/tex]=60.35[tex]\mathrm{cm}^{3}[/tex]
Result:
Thus the slant height and volume of tetrahedron are 6.53cm and 60.35[tex]\mathrm{cm}^{3}[/tex]
