Question

Ребяяят,помогите,пожалуйста,очень срочно!! Ребят,помогите,пожалуйста!!ОЧЕНЬ НУЖНО Боковая поверхность цилиндра в два раза больше площади его основания.Найдите объем цилиндра,если площадь его осевого сечения равна Q.

Answer 1

Sб=2πКр
Sосн=πR²
2πRh=2πR²⇒R=h
Sсеч=2Rh=2R²=Q
R=√(Q/2)
V=πR²h=πR³
V=πQ/2*√(Q/2)

Answer 2

Finding the Volume of a Cylinder with Doubled Lateral Surface Area

To find the volume of a cylinder when the lateral surface area is twice the area of its base, we need to use the formula for the lateral surface area of a cylinder and the formula for the volume of a cylinder.

The formula for the lateral surface area of a cylinder is given by:

Lateral Surface Area = 2πrh

where: - π (pi) is a mathematical constant approximately equal to 3.14159 - r is the radius of the base of the cylinder - h is the height of the cylinder

The formula for the volume of a cylinder is given by:

Volume = πr^2h

where: - π (pi) is a mathematical constant approximately equal to 3.14159 - r is the radius of the base of the cylinder - h is the height of the cylinder

Let's solve the problem step by step.

1. We are given that the lateral surface area of the cylinder is twice the area of its base. Mathematically, this can be expressed as:

2πrh = Q

where Q is the given area of the axial section.

2. We need to find the volume of the cylinder. Mathematically, this can be expressed as:

Volume = πr^2h

3. To find the volume, we need to eliminate the variable h from the equations. We can do this by solving the first equation for h:

h = Q / (2πr)

4. Now, substitute the value of h in the second equation:

Volume = πr^2(Q / (2πr))

Simplifying the equation:

Volume = (πr^2Q) / (2πr)

Canceling out the common terms:

Volume = Qr / 2

Therefore, the volume of the cylinder is Qr / 2.

Please note that the given search result snippet does not provide any relevant information for this specific problem. However, the solution provided above is derived from the standard formulas for the lateral surface area and volume of a cylinder.