Question

Боковая поверхность цилиндра в три раза больше площади его основания. Найдите отношение высоты цилиндра к радиусу его основания

Answer 1

Aбок=3*Аосн (по условию)

подставим формулы:

2П r h = 3* П r^2   l (сократим уравнения на П r)

2h=3r   h=3r\2 ; h\r = 3r\2 * 1\r = 3\2 = 1,5 (если записать все дробью, будет понятнее)

ответ:h\r = 1,5

Answer 2

Finding the Ratio of the Cylinder's Height to the Radius of its Base

To find the ratio of the height of a cylinder to the radius of its base, we need to use the given information that the lateral surface area of the cylinder is three times the area of its base.

Let's denote the height of the cylinder as H and the radius of its base as R.

The lateral surface area of a cylinder is given by the formula: S = 2πRH.

The area of the base of a cylinder is given by the formula: A = πR^2.

According to the given information, the lateral surface area of the cylinder is three times the area of its base. Mathematically, this can be expressed as:

2πRH = 3πR^2

To find the ratio of the height to the radius, we can simplify the equation:

2H = 3R

Dividing both sides of the equation by R, we get:

2H/R = 3

Therefore, the ratio of the height of the cylinder to the radius of its base is 2:3.

So, the height of the cylinder is two-thirds of the radius of its base.