Question

Около конуса описана сфера (сфера содержит окружность основания конуса и его вершину). Центр сферы совпадает с центром основания конуса. Образующая конуса равна 85√2. Найдите радиус сферы.

Answer 1

2r^2=(85 корней из 2)^2

r^2=7225

r=85

тк высота конуса равна радиусу сферы и радиус конуса=радиусу сферы,

то по теореме Пифагора можно найти радиус сферы

r^2+r^2= (85 корней из 2)^2

2r^2=7225*2

r^2=7225

r=85

 

Answer 2

Finding the Radius of the Sphere

To find the radius of the sphere, we can use the given information about the cone and the sphere it is circumscribed around.

The length of the generatrix of the cone is given as 85√2. We can use this information to calculate the radius of the sphere.

The relationship between the radius of the sphere (r) and the generatrix of the cone (l) is given by the formula: r = √(l^2 + (r/2)^2)

Where: - r = radius of the sphere - l = generatrix of the cone

Using this formula, we can calculate the radius of the sphere.

Calculation

Using the given generatrix of the cone (l = 85√2), we can substitute this value into the formula to find the radius of the sphere.

r = √((85√2)^2 + (r/2)^2)

Now, we can solve for the radius of the sphere.

Solution

r = √(7225*2 + (r/2)^2) This equation can be solved to find the value of r, the radius of the sphere.

Let's calculate the value of r using the given equation.