Question

Сумма трех измерений прямоугольного параллепипеда равна 52см. Его длина в 2 раза больше ширины, а высота в 4 раза меньше ширины. Найдите объём прямоугольного параллепипеда

Answer 1

Пусть х длина
тогда ширина будет равна 4х
длина будет равна 2*4х=8х
составим уровнение:
х+4х+8х=52
13х=52
х=52:13
х=4
4см -высота
4*4=16см-ширина
4*8=32см-длмна
V=4*16*32=2048см в кубе

Answer 2

Finding the Dimensions of the Rectangular Parallelepiped

To find the volume of a rectangular parallelepiped, we first need to determine its dimensions based on the given information.

Let's assume: - Length of the parallelepiped = L - Width of the parallelepiped = W - Height of the parallelepiped = H

According to the given information: - The sum of the three dimensions is 52 cm: L + W + H = 52 cm. - The length is twice the width: L = 2W. - The height is four times smaller than the width: H = W/4.

Calculating the Volume of the Rectangular Parallelepiped

The volume of a rectangular parallelepiped is calculated by multiplying its length, width, and height.

The formula for the volume of a rectangular parallelepiped is: Volume = Length * Width * Height

Substituting the given information into the formula: Volume = (2W) * W * (W/4) Volume = 2W^2 * (W/4) Volume = (W^3)/2

To find the value of W, we can substitute the value of H into the equation L + W + H = 52 cm: 2W + W + (W/4) = 52 cm

Simplifying the equation: (9W/4) = 52 cm 9W = 208 cm W = 208/9 cm

Substituting the value of W back into the volume formula: Volume = ((208/9)^3)/2

Calculating the volume using the given values: Volume ≈ 338.27 cm^3

Therefore, the volume of the rectangular parallelepiped is approximately 338.27 cm^3.