Question

Find the volume and total surface area of a regular tetrahedron whose measure of one edge is 10cm

Answer 1

The total surface area of a regular tetrahedron is calculated through the equation,
                            SA = (sqrt 3) x a²
Substituting the known value,
                            SA = (sqrt 3) x (10 cm)² = 173.20 cm²
Its volume is obtained by,
                             V = ((sqrt 2)/ 12) x a³
                         V = ((sqrt 2) / 12) x (10 cm)³ = 117.85 cm³
Thus, its surface area and volume are 173.20 cm² and 117.85 cm³, respectively.

Answer 2

For a tetrahedron, the total surface area is expressed as:
SA = √3 x a²
Substituting the given value,
SA = √3 x (10 cm)² = 173.20 cm²

The volume is expressed as,
V = (√2/ 12) x a³

Substituting the given values,
V = (√2 / 12) x (10 cm)³ = 117.85 cm³