Question

the length of each side of a regular tetrahydrone is 12cm , find the volume of the tetrahedron​

Answer 1

Given the length of each side of a regular tetrahedron is 12 cm

So A/Q we need to calculate out the volume of the tetrahydron So for calculating the volume we need to apply the volume formula of tetrahydron that is .

$\bold{\red{volume = \frac{a ^{3} }{6 \sqrt{2} } }}$

Here a is the sides of a tetrahydron

so let us calculate out the volume

$= > volume = \frac{a ^{3} }{6 \sqrt{2} } \\ \\ = >volume = \frac{12 ^{3} }{6 \times \sqrt{2} } \\ \\ = > volume = \frac{12 \times 12 \times 12}{6 \times 1.4} \\ \\ = > volume = \frac{1728}{8.4} \\ \\ = > volume =205.7cm ^{3}$

So from the above calculation we find the volume of the tetrahydron is 205.7 cm³