Question

Площадь боковой поверхности цилиндра равна 40П ,а диаметр 5.Найдите высоту цилиндра.?

Answer 1

$S=2*\pi*r*h$

r=5/2=2.5

h=S:(2*$\pi$*r)=$40\pi:(2*\pi*2,5)=$$40\pi:5\pi=8$cм-высота

Answer 2

Calculation of Cylinder Height

To find the height of a cylinder when the lateral surface area and diameter are given, we can use the formula for the lateral surface area of a cylinder:

Lateral Surface Area (S) = 2 * π * r * h

where: - S is the lateral surface area - π is a mathematical constant approximately equal to 3.14159 - r is the radius of the base of the cylinder - h is the height of the cylinder

In this case, we are given that the lateral surface area (S) is equal to 40π and the diameter is 5. We can use this information to find the radius (r) and then calculate the height (h).

Solution:

1. Calculate the radius (r) using the given diameter: - The diameter is given as 5, so the radius is half of the diameter: r = 5/2 = 2.5.

2. Substitute the values into the formula for the lateral surface area: - S = 2 * π * r * h - 40π = 2 * π * 2.5 * h

3. Simplify the equation by canceling out the common factors: - 40 = 2 * 2.5 * h - 40 = 5h

4. Solve for h by dividing both sides of the equation by 5: - h = 40/5 - h = 8

Therefore, the height of the cylinder is 8 units.

Answer:

The height of the cylinder is 8 units.