At the base of a rectangular parallelepiped with a side area of 120 lies a square with an area of 36.

univerkov | January 8, 2021 | education

At the base of a rectangular parallelepiped with a side area of 120 lies a square with an area of 36. Find the volume of the parallelepiped.

Let’s calculate the side length of the AВСD square at the base of the parallelepiped.
Sosn = AB ^ 2.
AB = √Sbase = √36 = 6 cm.
Determine the perimeter of the AВСD square.
Rosn = 4 * AB = 4 * 6 = 24 cm.
Let’s define the height of the parallelepiped through the area of the side surface.
Sside = АА1 * Rusn.
AA1 = S side / Rosn = 120/24 = 5 cm.
Let’s define the volume of the parallelepiped.
V = Sbn * AA1 = 36 * 5 = 180 cm3.
Answer: The volume of the parallelepiped is 180 cm3.

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