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Maurinko [17]
3 years ago
15

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

Mathematics
1 answer:
grigory [225]3 years ago
7 0

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

<u>Step by Step Explanation: </u>

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}

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