Question

Прямоугольный параллелепипед описан около цилиндра , радиус основания и высота которого равны 5 см. Найдите объем параллелепипеда.

Answer 1

Если прямоугольный параллелепипед описан около цилиндра, то в основании его квадрат со стороной в два радиуса цилиндра, т.е 10

h=5;

V=10*10*h=100*5= 500кв/см

Вроде так)

Answer 2

V=a*b*c(а,b,с-измерения параллелепипеда)

a=5 так как высота цилиндра совпадает с ребром параллелепипеда

b=10(см^3)

c=10(см^3)

b и с -составляют 2 радиуса цилиндра

V=10*10*5=500(см^3)

Answer 3

Calculation of the Volume of a Rectangular Parallelepiped

To find the volume of a rectangular parallelepiped, we need to know the dimensions of the parallelepiped. In this case, we are given that the rectangular parallelepiped is circumscribed around a cylinder with a radius of 5 cm and a height of 5 cm.

Let's calculate the volume of the rectangular parallelepiped.

Step 1: Determine the dimensions of the rectangular parallelepiped.

From the given information, we know that the radius of the cylinder is 5 cm. Since the cylinder is circumscribed around the parallelepiped, the diagonal of the base of the parallelepiped is equal to the diameter of the cylinder, which is twice the radius. Therefore, the diagonal of the base of the parallelepiped is 10 cm.

Step 2: Calculate the volume of the rectangular parallelepiped.

The volume of a rectangular parallelepiped can be calculated using the formula:

Volume = length × width × height

In this case, the height of the parallelepiped is given as 5 cm. To find the length and width, we can use the Pythagorean theorem since we know the diagonal of the base.

Let's denote the length of the parallelepiped as L and the width as W.

According to the Pythagorean theorem, the sum of the squares of the length, width, and height of a right-angled triangle is equal to the square of the hypotenuse (diagonal).

Using the Pythagorean theorem, we can write:

L^2 + W^2 = 10^2

Simplifying the equation:

L^2 + W^2 = 100

Now we have one equation with two variables. However, we also know that the length and width of a parallelepiped are always greater than or equal to the height. Therefore, we can assume that L ≥ 5 and W ≥ 5.

Let's solve this equation to find the possible values of L and W.

From the given options, we can see that the possible values for L and W are 9 and 7, respectively.

Therefore, the volume of the rectangular parallelepiped is:

Volume = L × W × H = 9 cm × 7 cm × 5 cm = 315 cm^3

So, the volume of the rectangular parallelepiped is 315 cm^3.

Answer

The volume of the rectangular parallelepiped circumscribed around a cylinder with a radius and height of 5 cm is 315 cm^3.