Question

Высота цилиндра 10 см.площадь сечения цилиндра плоскостью паралельна оси цилиндра и находящейся на расстаяние 6 см от нее = 160 см^2.вычислите площадь полной поверхности

Answer 1

160:10=16 -хорда

16:2=4-половина хорды

R= корень квадратный из (36+16)= корень квадратный из (52) 

 

 

 

 Sполной=2*пи*52+2*пи*10* корень квадратный из (52) =104*пи+40*пи*   корень квадратный из 13  

 

 

Answer 2

Calculating the Total Surface Area of a Cylinder

Given: - Height of the cylinder, h = 10 cm - Area of the cross-section of the cylinder parallel to its axis and located at a distance of 6 cm from the axis, A = 160 cm^2

To calculate the total surface area of the cylinder, we can use the formula: Total Surface Area = 2πrh + 2πr^2

Where: - r is the radius of the cylinder - h is the height of the cylinder

Calculating the Radius of the Cylinder

To find the radius of the cylinder, we can use the given area of the cross-section and the distance from the axis.

The area of the cross-section of the cylinder is given by the formula: A = πr^2

Solving for r: r = √(A/π)

Substituting the given value of A = 160 cm^2: r = √(160/π) r ≈ 7.99 cm

Calculating the Total Surface Area

Now that we have the value of r, we can calculate the total surface area of the cylinder using the formula: Total Surface Area = 2πrh + 2πr^2

Substituting the values: Total Surface Area = 2π * 7.99 * 10 + 2π * 7.99^2 Total Surface Area ≈ 2π * 7.99 * 10 + 2π * 63.84 Total Surface Area ≈ 159.8π + 127.68 Total Surface Area ≈ 687.34 cm^2

Answer

The total surface area of the cylinder is approximately 687.34 cm^2.