Find the volume, lateral surface area and total surface area of a regu

1.	Find the volume, lateral surface area and total surface area of a regular tetrahedron whose edge is 16 cm.
Answer» Volume of a regular tetrahedron = \(\frac{\sqrt{2}}{12} (edge)^2\) = \(\frac{\sqrt{2}}{12}\times 16^2\) = \(\frac{\sqrt{2}\times 256}{12} \) cm³ = \(\frac{64\sqrt{2}}{3} \) cm³ Lateral surface area = \(\frac{3\sqrt{3}}{4} (edge)^2 =\frac{3\sqrt{3}}{4} 16^2\) = 192\(\sqrt{3}\) cm² Total surface area =\({\sqrt{3}} (edge)^2 = {\sqrt{3}} \times 16^2\) cm² = 256\(\sqrt{3}\) cm²

Find the volume, lateral surface area and total surface area of a regular tetrahedron whose edge is 16 cm.

Answer»

Volume of a regular tetrahedron = \(\frac{\sqrt{2}}{12} (edge)^2\) = \(\frac{\sqrt{2}}{12}\times 16^2\)

= \(\frac{\sqrt{2}\times 256}{12} \) cm³ = \(\frac{64\sqrt{2}}{3} \) cm³

Lateral surface area = \(\frac{3\sqrt{3}}{4} (edge)^2 =\frac{3\sqrt{3}}{4} 16^2\)

= 192\(\sqrt{3}\) cm²

Total surface area =\({\sqrt{3}} (edge)^2 = {\sqrt{3}} \times 16^2\) cm² = 256\(\sqrt{3}\) cm²