Ask Question
10 February, 20:04

Determine the maximum ratio of the cross-sectional area of a hexagon vs. the area for the circle that contains such hexagon.

+2
Answers (1)
  1. 10 February, 20:13
    0
    the ratio of the area of the hexagon vs area of the circle that contains it is 0.8269

    Explanation:

    The area of a hexagon Ah expressed in terms of the distance from the centre to one of the vertex R is

    Ah = 6 * (area triangle with angle 2π/6) = 6 * (1/2) * R*R sin (2π/6) = 3*R²*√3/2 =

    (3/2) √3*R²

    the area of the circle Ac that contains such hexagon is

    Ac = π*R²

    the ratio of the area of the hexagon vs area of the circle is

    r = Ah/Ac = (3/2) √3*R² / (π*R²) = 3*√3 / (2*π) = 0.8269
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “Determine the maximum ratio of the cross-sectional area of a hexagon vs. the area for the circle that contains such hexagon. ...” in 📗 Engineering if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers