Question

15. The length of each edge of a regular tetrahedron,

Answer 1

Slant height of tetrahedron is=6.53cm

Volume of the tetrahedron is=60.35$\mathrm{cm}^{3}$

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=$\sqrt{\frac{2}{3}} a$

Where a= length of each edge

Slant height=$\sqrt{\frac{2}{3}} \times 8$

                     =$\sqrt{0.6667} \times 8$

                     =$0.8165 \times 8$=6.53cm

Similarly formula used for calculating volume is given as

Volume of the tetrahedron=$\frac{a^{3}}{6 \sqrt{2}}$

Substitute the value of a in above equation we get

Volume=$\frac{8^{5}}{6 \sqrt{2}}$

            =$\frac{512}{6 \sqrt{2}}$

            =$\frac{512}{6 \times 1.414}$

Volume=$512 / 8.484$=60.35$\mathrm{cm}^{3}$

Result:

Thus the slant height and volume of tetrahedron are 6.53cm and 60.35$\mathrm{cm}^{3}$