Question

the length of each edge of a regular tetrahedron,
itical equilateral triangles, is
The length of each edge of a regular tetra
whose faces are identical equilateral
8 cm. Find its
(i) slant height,
(ii) volume.
Hint: All sides are equal. The centre Cof an eq
al. The centre C of an equilateral
triangle is ? of its height h.
​

Answer 1

Answer:

Step-by-step explanation:

for that triangle, the Pythagorean theorem says

4^2+h^2=8^2

so, 16+h^2=64

h^2=64-16

h^2=48

√h^2= √48

h=6.93

Volume of a regular tetrahedron:

V = (√2/12)*L³ where L is the length of an edge.

If L = 8 cm then

V = ( √2/12 ) * 8³ ≈ (1,4142/12)*512 ≈ 60,3398 cm³