Question

Шар вписан в цилиндр.Площадь поверхности цилиндра равна 54. Найти площадь поверхности шара???

Answer 1

Пл. поверхности цилиндра описанного вокруг шара равна 

2nR^2 + 2nR *2R=6nR^2

площадь поверхности вписанного шара равна 4n*R^2

подставим значения 6nR^2=54   nR^2=9

т.о. площадь поверхности шара равна 4nR^2=4*9=36

Answer 2

Calculating the Surface Area of the Sphere Inscribed in a Cylinder

To find the surface area of the sphere inscribed in a cylinder, we can use the formula for the surface area of a sphere, which is given by the formula:

Surface Area of Sphere (A) = 4πr^2

Where r is the radius of the sphere.

The radius of the sphere can be found using the formula for the volume of a cylinder, which is given by the formula:

Volume of Cylinder (V) = πr^2h

Where r is the radius of the cylinder and h is the height of the cylinder.

We are given that the surface area of the cylinder is 54. We can use this information to find the radius of the sphere and then use it to calculate the surface area of the sphere.

Calculating the Radius of the Sphere

We can find the radius of the sphere by using the given surface area of the cylinder.

Given: Surface Area of Cylinder = 54

We can use the formula for the surface area of a cylinder to find the radius: Surface Area of Cylinder (A) = 2πrh + 2πr^2

Where r is the radius of the cylinder and h is the height of the cylinder.

Calculating the Surface Area of the Sphere

Once we have found the radius of the sphere, we can use it to calculate the surface area of the sphere using the formula: Surface Area of Sphere (A) = 4πr^2

Let's proceed with the calculations.

Calculations

Using the given surface area of the cylinder (54), we can solve for the radius of the sphere:

54 = 2πrh + 2πr^2

We can then use the radius of the sphere to calculate its surface area:

Surface Area of Sphere (A) = 4πr^2

Let's calculate the radius of the sphere and then its surface area.