Question

Высота конуса равна 24,а диаметр основания - 14. Найдите образующую конуса. Сделать чертеж.

Answer 1

Радиус основания равен 14 / 2 = 7 ед. Образующая конуса равна Корню квадратному из 24^2 + 7^2 = Корню квадратному из 576 +49 = Корню квадратному из 625 = 25 ед 

Answer 2

BO - 24
AC  - 20 
BC - искомая величина
AO = OC = $\frac{1}{2}$AC = 7
Треугольник BOC - прямоугольный, отсюда:
$BC^{2} = BO^{2} + OC^{2}$
BC^{2} = 576 + 49
$BC^{2}$ = 625
BC = 25

Answer 3

Finding the Slant Height of a Cone

To find the slant height of a cone, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In the case of a cone, the slant height is the hypotenuse of a right triangle, with the radius of the base as one of the legs and the height of the cone as the other leg.

Given that the height of the cone is 24 and the diameter of the base is 14, we can find the radius of the base by dividing the diameter by 2. So the radius is 14/2 = 7.

Using the Pythagorean theorem, we can calculate the slant height of the cone as follows:

Step 1: Calculate the square of the radius: 7^2 = 49.

Step 2: Calculate the square of the height: 24^2 = 576.

Step 3: Add the squares of the radius and height: 49 + 576 = 625.

Step 4: Take the square root of the sum to find the slant height: √625 = 25.

Therefore, the slant height of the cone is 25 units.

Diagram:

Here is a diagram to help visualize the cone:

         /|
        / |
       /  |
      /   |
     /    |
    /     |
   /______|

In the diagram, the vertical line represents the height of the cone, and the diagonal line represents the slant height.

I hope this helps! Let me know if you have any further questions.