Question

В цилиндре с высотой 6 см. проведено параллельное оси сечение, отстоящее от неё на расстоянии 4см. Найти радиус цилиндра если площадь сечения равна 36 см.в квадрате..

Answer 1

S se4enie=36, a h- 6, se4enie kvadrat to vse storony=6 см. Т.K. se4enie ostatet оt оsi na 4 sm, tо pо t. Pifagora r=sqrt(16+9)=sqrt25=5 sm.

Answer 2

Problem Analysis

We are given a cylinder with a height of 6 cm. A parallel section is made to the axis of the cylinder, which is 4 cm away from it. The area of the section is given as 36 cm². We need to find the radius of the cylinder.

Solution

To solve this problem, we can use the formula for the area of a circle, which is given by:

A = πr²

where A is the area and r is the radius of the circle.

Since the section is parallel to the axis of the cylinder, the section is also a circle. The given area of the section is 36 cm². Therefore, we can write the equation as:

36 = πr²

To find the radius, we need to isolate it in the equation. We can do this by dividing both sides of the equation by π:

36/π = r²

Taking the square root of both sides gives us:

√(36/π) = r

Simplifying the square root gives us:

r = √(36/π)

Now, let's calculate the value of r using the given information.

Calculation

Using the given information, we can calculate the value of r:

r = √(36/π)

Using a calculator, we can evaluate this expression:

r ≈ 3.02 cm

Therefore, the radius of the cylinder is approximately 3.02 cm.

Answer

The radius of the cylinder is approximately 3.02 cm.