Question

Пло­щадь бо­ко­вой по­верх­но­сти ци­лин­дра равна36п , а вы­со­та — 4. Най­ди­те диа­метр ос­но­ва­ния.

Answer 1

Sбок( для цилиндра) = 2ПRh

S=36П, d=4, значит R=4/2=2

Подставляем в форулу:

36П=2П*2*h, отсюда: 36П=4Пh. h=9.

Ответ: 6.

Answer 2

Calculation of the Diameter of the Base of a Cylinder

To find the diameter of the base of a cylinder, we need to use the given information about the surface area and height of the cylinder.

Let's break down the problem step by step:

1. We are given that the surface area of the lateral surface of the cylinder is 36 square units. - The surface area of the lateral surface of a cylinder is given by the formula: 2πrh, where r is the radius of the base and h is the height of the cylinder. - However, we are not given the radius of the base, so we need to find it.

2. We are also given that the height of the cylinder is 4 units.

To find the radius of the base, we can rearrange the formula for the surface area of the lateral surface of a cylinder:

2πrh = 36

Now, let's solve for the radius r:

r = 36 / (2πh)

Substituting the given value of h = 4, we can calculate the radius:

r = 36 / (2π * 4)

Using the value of π as approximately 3.14, we can simplify the equation:

r ≈ 36 / (2 * 3.14 * 4)

Calculating this expression, we find:

r ≈ 36 / 25.12 ≈ 1.43

Now that we have the radius of the base, we can calculate the diameter by multiplying the radius by 2:

d = 2 * r ≈ 2 * 1.43 ≈ 2.86

Therefore, the diameter of the base of the cylinder is approximately 2.86 units.

Please note that the calculations are approximate due to the use of an approximate value for π.