Question

Діагональ осьового перерізу циліндра дорівнює 17см а висота циліндра на 11 см більша за його радіус.Знайти площу особового перерізати циліндра

Answer 1

ДАНО
а = R+11
b = 2*R - диаметр
c = 17 см - диагональ.
НАЙТИ
S = 2*a*R - площадь сечения.
РЕШЕНИЕ
По т. Пифагора
(R+11)²+ (2*R)² = 17² = 289
R²+ 22*R + 121 + 4*R² - 289 = 0
5*R² + 22*R - 168 = 0
D = 3844, √1384 = 62
R = 4 см - радиус
a = 4+11 = 15 см - высота
S = 2*R*a = 8*15 = 120 см² - площадь сечения -  ОТВЕТ
http://prntscr.com/hgakjx - рисунок к задаче.

Answer 2

Problem Analysis

To find the surface area of the axial cross-section of a cylinder, we need to know the radius and height of the cylinder. In this case, we are given that the diagonal of the axial cross-section is 17 cm and the height of the cylinder is 11 cm greater than its radius.

Given Information

- Diagonal of the axial cross-section of the cylinder = 17 cm - Height of the cylinder = radius + 11 cm

Solution

Let's assume the radius of the cylinder is r cm. Since the height of the cylinder is 11 cm greater than its radius, the height can be expressed as r + 11 cm.

To find the surface area of the axial cross-section, we need to find the length of the diagonal of the axial cross-section. The diagonal of the axial cross-section is the hypotenuse of a right triangle formed by the radius, height, and diagonal.

Using the Pythagorean theorem, we can express the diagonal of the axial cross-section as:

diagonal^2 = radius^2 + height^2

Substituting the given values, we have:

17^2 = r^2 + (r + 11)^2

Simplifying the equation:

289 = r^2 + (r^2 + 22r + 121)

289 = 2r^2 + 22r + 121

2r^2 + 22r + 121 - 289 = 0

2r^2 + 22r - 168 = 0

Now, we can solve this quadratic equation to find the value of r.

Using the quadratic formula:

r = (-b ± √(b^2 - 4ac)) / (2a)

where a = 2, b = 22, and c = -168.

Solving the equation, we get two possible values for r. Let's calculate them:

r = (-22 ± √(22^2 - 4 * 2 * -168)) / (2 * 2)

r = (-22 ± √(484 + 1344)) / 4

r = (-22 ± √1828) / 4

r ≈ (-22 ± 42.8) / 4

So, the two possible values for r are approximately:

r ≈ 5.7 cm or r ≈ -11.2 cm

Since the radius cannot be negative, we discard the negative value.

Therefore, the radius of the cylinder is approximately 5.7 cm.

Now, we can calculate the height of the cylinder:

height = radius + 11

height ≈ 5.7 + 11

height ≈ 16.7 cm

Finally, we can calculate the surface area of the axial cross-section of the cylinder using the formula:

Surface Area = π * radius^2

Surface Area ≈ π * (5.7)^2

Surface Area ≈ 102.07 cm^2

Answer

The surface area of the axial cross-section of the cylinder is approximately 102.07 cm^2.