a sphere of radius 3m is circumscribed about a regular triangular prism. if the base edge of the prism is 2m, find the volume of the prism

Answer 1

The base of the prism is an equilateral triangle of side 2, so its altitude is √3.

The distance from thecenter of the triangle to a vertex is 2/3 of that, or 2/√3.

Now, the distance from the base of the prism to the center of the sphere is one side of a right triangle with hypotenuse=3, and the other side 2/√3, or √(23/3)

Thus, due to symmetry, the volume of the prism is the area of the base times 2√(23/3)