Question

В шаре на расстоянии 8 см. от центра проведено сечение, радиус которого 6 см. Найти объём и площадь соответствующей сферы?

Answer 1

Радиус шара найдем по теореме  Пифагора  R=sqrt*(64+36)=10 см, тогда V=4/3*П*R^3=4/3*П*1000=4000П/3

Answer 2

Problem Analysis

We are given that a section is made in a sphere at a distance of 8 cm from its center, and the radius of the section is 6 cm. We need to find the volume and surface area of the corresponding sphere.

Solution

To find the volume of the sphere, we can use the formula:

Volume of a sphere = (4/3) * π * r^3

where r is the radius of the sphere.

From the given information, we know that the radius of the section is 6 cm. Since the section is made at a distance of 8 cm from the center, the radius of the sphere is the sum of the radius of the section and the distance from the center to the section. Therefore, the radius of the sphere is 6 cm + 8 cm = 14 cm.

Using this radius, we can calculate the volume of the sphere:

Volume of the sphere = (4/3) * π * (14 cm)^3

To find the surface area of the sphere, we can use the formula:

Surface area of a sphere = 4 * π * r^2

Using the radius of the sphere, we can calculate the surface area:

Surface area of the sphere = 4 * π * (14 cm)^2

Let's calculate the volume and surface area of the sphere.

Calculation

Using the formulas mentioned above, we can calculate the volume and surface area of the sphere:

Volume of the sphere = (4/3) * π * (14 cm)^3

Surface area of the sphere = 4 * π * (14 cm)^2

Calculating the values:

Volume of the sphere = (4/3) * π * (14 cm)^3 = 4,389.33 cm^3

Surface area of the sphere = 4 * π * (14 cm)^2 = 2,463.02 cm^2

Therefore, the volume of the sphere is 4,389.33 cm^3 and the surface area of the sphere is 2,463.02 cm^2.

Answer

The volume of the corresponding sphere is 4,389.33 cm^3 and the surface area of the sphere is 2,463.02 cm^2.