Question

В цилиндр вписан шар( он касается оснований и боковой поверхности). Во сколько раз высота цилиндра больше его радиуса?

Answer 1

Насколько я понимаю, высота цилиндра - это диаметр шара, а радиусы у цилиндра и шара одинаковы. Следовательно, в 2 раза.

Answer 2

Calculating the Ratio of Cylinder Height to Radius

To find the ratio of the height of the cylinder to its radius when a sphere is inscribed within it, we can use the formula for the volume of a cylinder and the volume of a sphere.

The volume of a cylinder is given by the formula: V_cylinder = π * r^2 * h .

The volume of a sphere is given by the formula: V_sphere = (4/3) * π * r^3 .

When a sphere is inscribed in a cylinder, the diameter of the sphere is equal to the height of the cylinder, and the radius of the sphere is equal to the radius of the cylinder. Therefore, the diameter of the sphere is twice the radius of the cylinder.

Using the relationship between the volumes of the sphere and the cylinder, we can express the radius of the cylinder in terms of its height: V_cylinder = V_sphere π * r^2 * h = (4/3) * π * r^3 h = (4/3) * r .

So, the height of the cylinder is 4/3 times its radius.

Therefore, the ratio of the height of the cylinder to its radius when a sphere is inscribed within it is 4:3.