Asked by ameen
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
Answers
Answered by
Steve
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)
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)
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