Question

Прямоугольный параллелепипед описан около цилиндра, радиус основания и высота которого равны 6 см. Найдите объём параллелепипеда.

Answer 1

Основание параллелепипеда - квадрат
6*2=12(см) - сторона квадрата       (равна диаметру окружности)
V=авс
12*12*6=864(см3) - объем параллелепипеда

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 three sides: length, width, and height. In this case, we are given that the rectangular parallelepiped is circumscribed around a cylinder with a radius of 6 cm and a height of 6 cm.

Let's denote the length, width, and height of the rectangular parallelepiped as L, W, and H, respectively.

To find the volume, we can use the formula:

Volume = Length × Width × Height

Since the rectangular parallelepiped is circumscribed around a cylinder, we can use the properties of a cylinder to find the dimensions of the parallelepiped.

The radius of the cylinder is given as 6 cm. We know that the diameter of the cylinder is twice the radius, so the diameter of the cylinder is 12 cm.

The height of the cylinder is also given as 6 cm.

Now, let's find the dimensions of the rectangular parallelepiped using the properties of the cylinder:

1. The length (L) of the parallelepiped is equal to the diameter of the cylinder, which is 12 cm. 2. The width (W) of the parallelepiped is equal to the circumference of the cylinder, which can be calculated using the formula: Circumference = 2 × π × Radius. Substituting the given radius of 6 cm, we get: Circumference = 2 × π × 6 = 12π cm. 3. The height (H) of the parallelepiped is equal to the height of the cylinder, which is 6 cm.

Now, we can substitute these values into the volume formula to find the volume of the rectangular parallelepiped:

Volume = Length × Width × Height = 12 cm × (12π cm) × 6 cm = 864π cm³.

Therefore, the volume of the rectangular parallelepiped is 864π cm³.

Please note that the value of π (pi) is approximately 3.14159.