The height of a rectangular parallelepiped is 20 cm, which is 5 cm more than its width and 3 times less than its length. Calculate the surface area of the parallelepiped.
Since the area of a parallelepiped is calculated through the length of its edges by the formula:
S = 2 * (a * b + b * c + a * c), where a, b, c, = the length of its edges.
1. Knowing that the width is 5 cm less than the height and the height of the rectangular parallelepiped is 20 cm, we calculate the width.
20 – 5 = 15 cm
2. By condition, the length is 3 times greater than the height, we calculate it too.
20 * 3 = 60 cm.
3. Knowing the length, width and height and substituting their values into the formula, you can calculate the volume of a rectangular parallelepiped.
S = 2 * (a * b + b * c + a * c) = 2 * (20 * 15 + 20 * 60 + 15 * 60)
S = 2 * (300 + 1200 + 900) = 2 * 2400 = 4800 cm3.
Answer: 4800 cm3.
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