Question

Квадрат ,площадь которого 625см (в квадрате ) ,вращается вокруг своей стороны.Найдите образующую, высоту, радиус, площадь основания и длину окружности основания получившегося цилиндра . Помогите пожалуйста . новая тема и не могу понять как решить

Answer 1

Для начала ищем сторону квадрата:

 

$a=\sqrt{625}=25cm$

 

сторона а одновременно является высотой, образующей цилиндра, а также радиусом основания цилиндра = 25 см

 

Площадь основания:

 

$S=\pi*r^{2}=3,14*625=1962,5 cm^{2}$

 

Длина окружности:

 

$L=2*\pi*r=2*3,14*25=157cm$

 

 

 

 

 

Answer 2

Problem Analysis

We are given a square with an area of 625 cm² that is rotating around one of its sides. We need to find the slant height (or generatrix), height, radius, base area, and circumference of the resulting cylinder.

Solution

To solve this problem, we can follow these steps: 1. Find the length of one side of the square. 2. Calculate the slant height (or generatrix) of the resulting cylinder. 3. Determine the height of the cylinder. 4. Calculate the radius of the cylinder. 5. Find the base area of the cylinder. 6. Calculate the circumference of the base of the cylinder.

Let's go through each step in detail.

Step 1: Find the length of one side of the square

The area of the square is given as 625 cm². To find the length of one side, we can take the square root of the area. The length of one side of the square is 25 cm.

Step 2: Calculate the slant height (or generatrix) of the resulting cylinder

The slant height (or generatrix) of a cylinder is the distance from the top of the cylinder to the base along the curved surface. In this case, the slant height is equal to the length of one side of the square. The slant height of the resulting cylinder is 25 cm.

Step 3: Determine the height of the cylinder

The height of the cylinder is equal to the length of one side of the square. The height of the resulting cylinder is 25 cm.

Step 4: Calculate the radius of the cylinder

The radius of the cylinder can be found by dividing the length of one side of the square by 2. The radius of the resulting cylinder is 12.5 cm.

Step 5: Find the base area of the cylinder

The base area of a cylinder is given by the formula: base area = π * radius². Substituting the value of the radius, we can calculate the base area of the cylinder. The base area of the resulting cylinder is approximately 490.87 cm².

Step 6: Calculate the circumference of the base of the cylinder

The circumference of the base of a cylinder is given by the formula: circumference = 2 * π * radius. Substituting the value of the radius, we can calculate the circumference of the base of the cylinder. The circumference of the base of the resulting cylinder is approximately 78.54 cm.

Summary

Based on the given information, the properties of the resulting cylinder are as follows: - Slant height (or generatrix): 25 cm - Height: 25 cm - Radius: 12.5 cm - Base area: approximately 490.87 cm² - Circumference of the base: approximately 78.54 cm

I hope this helps! Let me know if you have any further questions.