Question

Объём прямоугольного параллелепипеда равен 180 дм3 а 2 его измерения-6дм и 15дм. Найти сумму длин всех рёбер пар-педа. Дам 20 баллов!

Answer 1

V = a*b*c
V = 180 дм^3
a= 6 дм
b=15 дм
c=V/a*b
C=180/6*5 = 180/30 = 18/3 = 6 дм
S = 4*(a+b+c)
S=4*(6+6+15)=4*(12+15)=4*27=108 дм 

Answer 2

Calculation of the Volume of a Rectangular Parallelepiped

To find the sum of the lengths of all edges of a rectangular parallelepiped, we first need to calculate the volume of the parallelepiped.

Given: - Volume of the parallelepiped = 180 dm³ - Length of one dimension = 6 dm - Length of another dimension = 15 dm

The volume of a rectangular parallelepiped is calculated by multiplying the lengths of its three dimensions. In this case, we have two dimensions given, so we need to find the third dimension.

Let's assume the third dimension is "x" dm.

The volume of the parallelepiped can be expressed as:

Volume = Length × Width × Height

Substituting the given values:

180 dm³ = 6 dm × 15 dm × x dm

To find the value of "x", we can rearrange the equation:

x = 180 dm³ / (6 dm × 15 dm)

Simplifying the equation:

x = 180 dm³ / 90 dm²

x = 2 dm

Therefore, the third dimension of the parallelepiped is 2 dm.

Calculation of the Sum of the Lengths of All Edges

To find the sum of the lengths of all edges of the parallelepiped, we need to consider that a rectangular parallelepiped has 12 edges.

Each edge consists of two dimensions. In this case, we have three dimensions: 6 dm, 15 dm, and 2 dm.

The sum of the lengths of all edges can be calculated as:

Sum of lengths of all edges = 2 × (Length + Width + Height)

Substituting the given values:

Sum of lengths of all edges = 2 × (6 dm + 15 dm + 2 dm)

Sum of lengths of all edges = 2 × (23 dm)

Sum of lengths of all edges = 46 dm

Therefore, the sum of the lengths of all edges of the rectangular parallelepiped is 46 dm.

I hope this helps! Let me know if you have any further questions.