Question

Цилиндр с радиусом основания 3 см диагональ осевого сечения равно 10см. найти высоту цилиндра,площадь осевого сечения

Answer 1

h =корень квадратный из диагонали в квадрате вычесть диаметр в квадрате= корень из 100-36= корень из 64=8 см

S=6*8=48см.кв.

Answer 2

Calculation of Cylinder Height and Area of Cross-Section

To find the height of the cylinder and the area of its cross-section, we can use the given information about the radius of the base and the diagonal of the axial section.

Let's break down the solution step by step:

1. We are given that the radius of the base of the cylinder is 3 cm and the diagonal of the axial section is 10 cm.

2. We can use the Pythagorean theorem to find the height of the cylinder. The diagonal of the axial section is the hypotenuse of a right triangle formed by the radius and the height of the cylinder. The formula for the Pythagorean theorem is:

d^2 = r^2 + h^2

where d is the diagonal, r is the radius, and h is the height.

Plugging in the given values, we have:

10^2 = 3^2 + h^2

Solving for h, we get:

h^2 = 10^2 - 3^2 = 100 - 9 = 91

Taking the square root of both sides, we find:

h = √91 ≈ 9.54 cm

Therefore, the height of the cylinder is approximately 9.54 cm.

3. To calculate the area of the cross-section, we can use the formula for the surface area of the cylinder. The formula is:

S = 2πrh + 2πr^2

where S is the surface area, r is the radius, and h is the height.

Plugging in the given values, we have:

S = 2π(3)(9.54) + 2π(3)^2

Simplifying, we get:

S = 2π(28.62) + 2π(9) = 57.24π + 18π ≈ 75.24π

Therefore, the area of the cross-section is approximately 75.24π square cm.

In summary, the height of the cylinder is approximately 9.54 cm and the area of the cross-section is approximately 75.24π square cm.