In a rectangular parallelepiped, the length is 7 cm less than the width and 7 cm more than the height.
| February 12, 2021 | education
In a rectangular parallelepiped, the length is 7 cm less than the width and 7 cm more than the height. Surface area – 144 cm2. Find the volume of the parallelepiped.
Let side AB = X cm, Then AD = (X + 7) cm, and AA1 = (X – 7) cm.
The total surface area of a parallelepiped is:
S = 2 * (AB * AD + AB * AA1 + AD * AA1) = 286 cm2.
143 = (X * (X + 7) + X * (X – 7) + (X – 7) * (X + 7)).
143 = X2 + 7 * X + X ^ 2 – 7 * X + X ^ 2 – 49.
3 * X2 = 143 + 49 = 192.
X2 = 64.
X = AB = 8 cm, AD = 8 + 7 = 15 cm, AA1 = 8 – 7 = 1 cm.
Let’s define the volume of the parallelepiped. V = AB * AD * AA1. = 8 * 15 * 1 = 120 cm3.
Answer: The volume is 120 cm3.
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