The base of a straight parallelepiped is a rhombus whose area is 8 dm ^ 2.
| September 4, 2021 | education
The base of a straight parallelepiped is a rhombus whose area is 8 dm ^ 2. The areas of the diagonal sections are 24dm ^ 2 and 48dm ^ 2. find the volume of the parallelepiped.
Since there is a rhombus at the base of the parallelepiped, its area is equal to:
Sosn = ВD * АС / 2.
АС * ВD = 2 * Sсн = 2 * 8 = 16 dm2.
Diagonal sections are rectangles, then
Sаа1с1с = АА1 * АС = 48 dm2.
AC = 48 / AA1.
Svv1d1d = BD * AA1 = 24 dm2.
BD = 24 / AA1.
AC * BD = 578 / AA12.
AA12 = 578 / AC * BD = 576/16 = 36.
AA1 = 6 dm.
Then V = Sosn * AA1 = 8 * 6 = 48 dm3.
Answer: The volume of the parallelepiped is 48 dm3.
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