Question

В прямоугольном параллелепипеде длина в 2 раза больше ширины , а высота в 4 раза больше ширины . Найдите измерения прямоугольного параллелепипеда, если его объём равен 1000 см в Кубе. РЕШИТЕ ПОЖАЛУЙСТА!!!

Answer 1

Пусть длина, ширина и высота соответственно равны a,b,c.Тогда a=2b, c=4b, в то же время 2b*b*4b=1000, отсюда b=5, a=10, c=20.

Answer 2

Problem Analysis

We are given that the length of a rectangular parallelepiped is twice the width, and the height is four times the width. We need to find the dimensions of the parallelepiped if its volume is 1000 cubic centimeters.

Solution

Let's assume that the width of the parallelepiped is x centimeters. According to the given information, the length is twice the width, so the length is 2x centimeters. Similarly, the height is four times the width, so the height is 4x centimeters.

The volume of a rectangular parallelepiped is given by the formula: Volume = Length × Width × Height.

Substituting the values we have: 1000 = (2x) × x × (4x).

Simplifying the equation: 1000 = 8x^3.

Dividing both sides by 8: 125 = x^3.

Taking the cube root of both sides: x = 5.

Therefore, the width of the parallelepiped is 5 centimeters. The length is twice the width, so the length is 2 × 5 = 10 centimeters. The height is four times the width, so the height is 4 × 5 = 20 centimeters.

Hence, the dimensions of the rectangular parallelepiped are: - Width: 5 centimeters - Length: 10 centimeters - Height: 20 centimeters.

Answer

The dimensions of the rectangular parallelepiped are: - Width: 5 centimeters - Length: 10 centimeters - Height: 20 centimeters.

Please let me know if you need any further assistance!