Question

Ширина прямоугольника паралепипида 12 дм она в 2 раза меньше длины а высота больше шерены на 5 см найдите площадь поверхности паралепипеда и его объем

Answer 1

1)12*2=24 дм длина; 2)12+5=17 дм высота; 3)(24*12)*2=576 дм^2 площадь оснований; 4)(24*17)*2=816дм^2 боковые стороны; 5)(12*17)*2=408 дм^2 торцевые стороны; 6)576+816+408=1800дм^2 ПЛОЩАДЬ параллелепипеда; 7)12*24*17=4896дм^3 ОБЬЕМ параллелепипеда

Answer 2

Calculation of the Surface Area and Volume of a Parallelepiped

To find the surface area and volume of a parallelepiped, we need to know its dimensions. Let's break down the given information:

- The width of the parallelepiped is 12 dm. - The width is 2 times smaller than the length. - The height is greater than the width by 5 cm.

Let's calculate the length, width, and height of the parallelepiped based on the given information:

1. Width: The width is given as 12 dm. 2. Length: The width is 2 times smaller than the length. Therefore, the length is 2 times the width, which is 2 * 12 dm = 24 dm. 3. Height: The height is greater than the width by 5 cm. Since 1 dm is equal to 10 cm, the height is 12 cm greater than the width. Therefore, the height is 12 cm + 5 cm = 17 cm.

Now that we have the dimensions of the parallelepiped, we can calculate its surface area and volume.

Surface Area of the Parallelepiped

The surface area of a parallelepiped can be calculated by finding the sum of the areas of its six faces. The formula for the surface area of a parallelepiped is:

Surface Area (S) = 2(ab + bc + ac)

Where: - a, b, and c are the lengths of the three edges of the parallelepiped.

In our case, the lengths of the edges are: - a = 12 dm - b = 24 dm - c = 17 cm (converted to dm, which is 1.7 dm)

Let's substitute these values into the formula to calculate the surface area:

S = 2(12 * 24 + 24 * 1.7 + 12 * 1.7) dm²

Simplifying the equation:

S = 2(288 + 40.8 + 20.4) dm²

S = 2(349.2) dm²

S = 698.4 dm²

Therefore, the surface area of the parallelepiped is 698.4 dm².

Volume of the Parallelepiped

The volume of a parallelepiped can be calculated by finding the product of its three dimensions. The formula for the volume of a parallelepiped is:

Volume (V) = a * b * c

Where: - a, b, and c are the lengths of the three edges of the parallelepiped.

In our case, the lengths of the edges are: - a = 12 dm - b = 24 dm - c = 17 cm (converted to dm, which is 1.7 dm)

Let's substitute these values into the formula to calculate the volume:

V = 12 * 24 * 1.7 dm³

V = 489.6 dm³

Therefore, the volume of the parallelepiped is 489.6 dm³.

To summarize: - The surface area of the parallelepiped is 698.4 dm². - The volume of the parallelepiped is 489.6 dm³.

Please note that the calculations are based on the given information and assumptions made about the conversion of units.