15. the length of each edge of a regular tetrahedron,
whose faces are identical equilateral triangles, is
8 cm. find its
(i) slant height
(ii) volume.
hint: all sides are equal. the centre of an equilateral
triangle is of its height h.

Slant height of tetrahedron is=6.53cm

Volume of the tetrahedron is=60.35

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=

Where a= length of each edge

Slant height=

                     =

                     ==6.53cm

Similarly formula used for calculating volume is given as

Volume of the tetrahedron=

Substitute the value of a in above equation we get

Volume=

            =

            =

Volume==60.35

Result:

Thus the slant height and volume of tetrahedron are 6.53cm and 60.35

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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