Question

помогите с решением!!!Диагональ правильной четырехугольной призмы равна 4 см и наклонена к плоскости основания под углом 45 градусов. Найдите площадь боковой поверхности цилиндра, вписанного в эту призму

Answer 1

Высота призмы Н = d * sin v, диагональ основания D = d * cos v 

Сторона основания a = D / √ 2 = d * cos v / √ 2 

Площадь боковой поверхности 

Sб = P * H = 4 * a * H = 4 * d * cos v / √ 2 * d * sin v = 2 * √ 2 * d² * sin v * cos v = 

√ 2 * d² * sin 2v 

Осталось только подставить и все)) v-это угол(45), d- это диагональ(4)! √ -это корень)) УДАЧИ!!

Answer 2

Problem Analysis

We are given a right quadrangular prism with a diagonal of 4 cm, inclined to the base plane at an angle of 45 degrees. We need to find the lateral surface area of the cylinder inscribed in this prism.

Solution

To find the lateral surface area of the inscribed cylinder, we need to find the height and radius of the cylinder.

Let's start by finding the height of the cylinder. The height of the cylinder is equal to the height of the prism. Since the prism is right, the height of the prism is equal to the length of the diagonal. Therefore, the height of the cylinder is 4 cm.

Next, let's find the radius of the cylinder. To do this, we need to find the length of the side of the base of the prism.

Since the prism is right, the base of the prism is a square. Let's denote the length of the side of the square as s.

To find s, we can use the fact that the diagonal of the prism is equal to the hypotenuse of the right triangle formed by the side of the square and the height of the prism.

Using the Pythagorean theorem, we can write the following equation:

s^2 + s^2 = 4^2

Simplifying the equation, we get:

2s^2 = 16

Dividing both sides by 2, we get:

s^2 = 8

Taking the square root of both sides, we