The base of a straight prism is a rectangle with an alpha angle between the diagonals.
| May 15, 2021 | education
The base of a straight prism is a rectangle with an alpha angle between the diagonals. The diagonal of the prism is equal to d and forms a betta angle with the base plane. Find the volume of the figure.
In a right-angled triangle ACC1, Cosβ = AC / AC1.
AC = AC1 * Cosβ = d * Cosβ.
Sinβ = CC1 / AC1.
CC1 = AC1 * Sinβ = d * Sinβ.
Determine the area of the base of the prism.
Sb = АС2 * Sinα / 2 = d2 * Cos2β * Sinα / 2 cm2.
Let’s define the volume of the prism.
V = Ssc * CC1 = (d2 * Cos2β * Sinα / 2) * d * Sinβ = d3 * Cos2β * Sinα * Sinβ / 2 cm3.
Answer: The volume of the prism is d3 * Cos2β * Sinα * Sinβ / 2 cm3.
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