Question

площадь боковой поверхности цилиндра равна 16п , а диаметр основания равен 9 .найдите высоту цилиндра

Answer 1

$S_b_o_k=2 \pi R h=\pi d h=\pi*9*h=16 \pi$

$h=\frac{16 \pi}{\pi *9}=\frac{16}{9}$

Answer 2

Calculating the Height of a Cylinder

To find the height of the cylinder, we can use the formula for the lateral surface area of a cylinder, which is given by the formula S = 2 * π * r * h, where S is the lateral surface area, π is a constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cylinder.

Given that the lateral surface area of the cylinder is 16π and the diameter of the base is 9, we can calculate the height using the following steps:

1. Calculate the radius of the base using the formula radius = diameter / 2. 2. Substitute the values of the lateral surface area and radius into the formula S = 2 * π * r * h and solve for h.

Calculation

1. Calculating the Radius: - The radius of the base, r, is half the diameter, so r = 9 / 2. - Therefore, r = 4.5.

2. Using the Formula for Lateral Surface Area: - The lateral surface area, S, is given as 16π. - Substituting the values of S and r into the formula S = 2 * π * r * h: - 16π = 2 * π * 4.5 * h.

3. Solving for the Height (h): - Dividing both sides of the equation by 2π * 4.5 gives: - h = 16π / (2 * π * 4.5). - Simplifying, we get: - h = 16 / (2 * 4.5). - h = 16 / 9. - h = 1.777... (rounded to three decimal places).

Conclusion

The height of the cylinder is approximately 1.777 units.