Question

Площадь сечения шара плоскостью равна 20 п , а расстояние от центра шара до секущей плоскости равно 4. Найти обьем шара

Answer 1

S=pi*r^2
r^2=S/pi
R=корень(L^2+r^2)=корень(L^2+S/pi)
V=4/3*pi*R^3=4/3*pi*(L^2+S/pi)^(3/2)=4/3*pi*(4^2+20*pi/pi)^(3/2)=288*pi ~ 904,77868

Answer 2

Сечение с центром Е находится на расстоянии 4 см от центра О  шара.
Площадь сечения 20π 
Объем шара найдем по формуле  
V=(4πR³):3 
Сделаем рисунок к задаче.  
ОЕ - расстояние от центра шара до сечения,
r- радиус  сечения,
R - радиус шара.  
Треугольник ОЕК - прямоугольный, т.к. расстояние измеряется  перпендикуляром, и ОЕ перпендикулярен ЕК.  
 R найдем по т.Пифагора. Он равен 6 
V=4π*216:3=288π 

Answer 3

Calculation of the Volume of a Sphere

To find the volume of a sphere, we need to know the radius of the sphere. However, in this case, we are given the area of the cross-section of the sphere and the distance from the center of the sphere to the cutting plane.

Let's denote the radius of the sphere as r. The area of the cross-section of the sphere is given as 20 square units, and the distance from the center of the sphere to the cutting plane is given as 4 units.

To find the radius of the sphere, we can use the formula for the area of a circle:

Area of a circle = π * r^2

Since the cross-section of the sphere is a circle, we can equate the area of the cross-section to the area of a circle:

20 = π * r^2

Now, let's solve for the radius r:

r^2 = 20 / π

r = √(20 / π)

Now that we have the radius of the sphere, we can calculate its volume using the formula:

Volume of a sphere = (4/3) * π * r^3

Substituting the value of r into the formula, we get:

Volume = (4/3) * π * (√(20 / π))^3

Simplifying the expression, we have:

Volume = (4/3) * π * (20 / π)^(3/2)

Now, let's calculate the volume using the given values:

Volume = (4/3) * π * (20 / π)^(3/2)

Volume = (4/3) * π * (20 / π)^(3/2) cubic units

Please note that the exact numerical value of the volume will depend on the precise value of π used in the calculation.