Question

find the volume of a regular tetrahedron whose face is an equilateral triangle of side . the tetrahedron has height ℎ=23⎯⎯⎯⎯√.

Answer 1

To find the volume of a regular tetrahedron, you can use the formula V = (1/3) * Bh, where B is the area of the base and h is the height. The area of an equilateral triangle can be found using the formula A = (sqrt(3)/4) * s^2.

Step-by-step explanation:

To find the volume of a regular tetrahedron, we can use the formula for the volume of a pyramid: V = (1/3) * Bh, where B is the area of the base and h is the height. In this case, the base is an equilateral triangle with side length s. The area of an equilateral triangle can be found using the formula: A = (sqrt(3)/4) * s^2.

Given that the side length of the triangle is s and the height is h, we can substitute these values into the formulas to find the volume:

1. Find the area of the base using the formula A = (sqrt(3)/4) * s^2
2. Substitute the area and height into the volume formula: V = (1/3) * (A * h)
3. Simplify the expression to find the final volume of the tetrahedron.