The volume of a rectangular parallelepiped is 84 cm3. This parallelepiped was divided into two parts.
The volume of a rectangular parallelepiped is 84 cm3. This parallelepiped was divided into two parts. find the volume of each part if: a) the volume of one part is 6 times the volume of the other; b) the volume of one part is 40 cm3 more than the volume of the other part.
a) Let the volume of the first part of the parallelepiped be x cm ^ 3, then the volume of the second part is 6x cm ^ 3.
x + 6x = 84;
7x = 84;
x = 84/7;
x = 12.
If x = 12, then the volume of the first part is 12 cm ^ 3, and the second is 72 cm ^ 3.
Answer: 12 cm ^ 3 and 72 cm ^ 3.
b) Let the volume of the first part of the parallelepiped be x cm ^ 3, then the volume of the second part is (x + 40) cm ^ 3.
x + x + 40 = 84;
2x = 84 – 40;
2x = 44;
x = 22.
If x = 22, then the volume of the first part is 22 cm ^ 3, and the second is 62 cm ^ 3.
Answer: 22 cm ^ 3 and 62 cm ^ 3.