Question

Площадь поверхности цилиндра вдвое больше площади основания, площадь полной поверхности 500П см2. Найти размеры цилиндра

Answer 1

Исходя из условия делаем вывод, что Sполн=4Sосн=4ПR^2
R=5$\sqrt{5}$
Sбок=2Sосн
следовательно h=R

Answer 2

Finding the Dimensions of a Cylinder

To find the dimensions of a cylinder when the surface area is twice the area of the base and the total surface area is 500 square centimeters, we can use the following steps:

1. Let's assume the radius of the base of the cylinder is r and the height of the cylinder is h.

2. The formula for the surface area of a cylinder is given by: S = 2πrh + 2πr^2, where S is the total surface area, π is a mathematical constant approximately equal to 3.14159, r is the radius, and h is the height.

3. We are given that the surface area is twice the area of the base, so we can write the equation as: 2πr^2 = πrh.

4. Rearranging the equation, we get: r = 2h.

5. Substituting this value of r into the equation for the surface area, we have: S = 2π(2h)h + 2π(2h)^2.

6. Simplifying the equation, we get: S = 4πh^2 + 8πh^2.

7. Combining like terms, we have: S = 12πh^2.

8. We are given that the total surface area is 500 square centimeters, so we can write the equation as: 500 = 12πh^2.

9. Solving for h, we divide both sides of the equation by 12π: h^2 = 500 / (12π).

10. Taking the square root of both sides, we find: h = √(500 / (12π)).

11. Now that we have the value of h, we can substitute it back into the equation r = 2h to find the value of r.

12. Finally, we have the dimensions of the cylinder: radius (r) = 2h and height (h) = √(500 / (12π)).

Please note that the exact numerical values for the radius and height will depend on the specific calculations.