Question

Объем прямоугольного параллелепипеда равен 108. Чему будет равен объем параллелепипеда, если каждое его ребро уменьшить в три раза??

Answer 1

Решение на фото.........

Answer 2

Calculation of the Volume of a Rectangular Parallelepiped

To find the volume of a rectangular parallelepiped, we need to know the dimensions of its edges. In this case, the volume of the parallelepiped is given as 108. We are asked to determine the volume of the parallelepiped if each of its edges is reduced by a factor of three.

Let's denote the original dimensions of the parallelepiped as length (L), width (W), and height (H). The volume (V) of a rectangular parallelepiped is calculated using the formula:

V = L * W * H

Given that the volume of the parallelepiped is 108, we can write the equation:

108 = L * W * H Now, we are asked to find the volume of the parallelepiped when each of its edges is reduced by a factor of three. This means that the new dimensions of the parallelepiped will be L/3, W/3, and H/3.

Let's denote the new dimensions as L', W', and H'. The volume of the new parallelepiped can be calculated using the formula:

V' = (L/3) * (W/3) * (H/3)

Simplifying this equation, we get:

V' = (L * W * H) / (3 * 3 * 3)

Substituting the value of the original volume (108) into the equation, we have:

V' = (108) / (3 * 3 * 3)

Calculating this expression, we find:

V' = 108 / 27 = 4 Therefore, the volume of the parallelepiped, when each of its edges is reduced by a factor of three, is 4.

Conclusion

The volume of the rectangular parallelepiped is 108. When each of its edges is reduced by a factor of three, the volume of the new parallelepiped is 4.