Question

В цилиндре радиуса 6см диагональ осевого сечения равна 13см.Найдите площадь полной поверхности цилиндра.

Answer 1

Диаметр цилиндра равна 2R  2*6=12   R-радиус

найдем высоту по теореме пифагора 

a^2+b^2=c^2    b-высота

12^2+b^2=13^2

144+b^2=169

b=169-144=25=5

b=5

S=Пr(r+h)

S=2П6(6+5)

S=132П

ответ 132

Answer 2

Calculation of the Cylinder's Surface Area

To find the surface area of a cylinder, we need to consider the two circular bases and the curved surface area.

Let's denote the radius of the cylinder as r and the diagonal of the axial section as d.

Given that the radius of the cylinder is 6 cm and the diagonal of the axial section is 13 cm, we can use the Pythagorean theorem to find the height of the cylinder.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal of the axial section is the hypotenuse, and the radius and height of the cylinder are the other two sides.

Let's denote the height of the cylinder as h.

Using the Pythagorean theorem, we have:

d^2 = r^2 + h^2

Substituting the given values, we get:

13^2 = 6^2 + h^2

Simplifying the equation:

169 = 36 + h^2

h^2 = 169 - 36

h^2 = 133

Taking the square root of both sides, we find:

h = √133

Now that we have the height of the cylinder, we can calculate the surface area.

The surface area of a cylinder is given by the formula:

Surface Area = 2πr^2 + 2πrh

Substituting the given values, we have:

Surface Area = 2π(6^2) + 2π(6)(√133)

Simplifying the equation:

Surface Area = 72π + 12π√133

Therefore, the surface area of the cylinder is 72π + 12π√133 square centimeters.

Please note that the exact numerical value of the surface area depends on the value of π (pi), which is approximately 3.14159.