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Krawędź podstawy graniastoslupa prawidłowego sześciokątnego ma długość 4. Dlužsza przekątna w tym graniastoslupie tworzy z podstawą kąt o mierze .
Dokończ zdania. Wybierz wlaściwą odpowiedź spośród A-D oraz spośród E-H.
  1. Objętość tego graniastosłupa jest równa:
    A.
    B.
    C.
    D.
  2. Tangens kąta między krótszą przekątną tego graniastoslupa a jego podstawą jest równy:
    E. 1
    F.
    G.
    H.

Ask by Ruiz Luna. in Poland
Jan 22,2025

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  1. Objętość graniastosłupa wynosi .
  2. Tangens kąta między krótszą przekątną a podstawą wynosi .

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Beyond the Answer

Aby obliczyć objętość graniastosłupa prawidłowego sześciokątnego, musimy wykorzystać wzór na objętość , gdzie to pole podstawy, a to wysokość. Pole podstawy sześciokąta wynosi , gdzie to długość krawędzi. W naszym przypadku , więc pole wynosi . Wysokość można obliczyć z kąta i dłuższej przekątnej. Ostateczna objętość wynosi .
Tangens kąta między krótszą przekątną a podstawą graniastosłupa możemy obliczyć na podstawie jego wysokości oraz długości podstawy. Ponieważ wysokość graniastosłupa jest proporcjonalna do długości długiej przekątnej i tworzy kąt z podstawą, co prowadzi nas do wartości 1, ponieważ .

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