Question

Прямокутник зi сторонами 8 см i 7 см обертається навколо меншої сторони. Знайдіть висоту, радіyc і діаметр утвореного циліндра.

Answer 1

Ответ:

8 см

Объяснение:

ответ проверенный))))

Answer 2

Problem Analysis

We are given a rectangle with sides measuring 8 cm and 7 cm. The rectangle is rotated around its shorter side. We need to find the height, radius, and diameter of the resulting cylinder.

Solution

To solve this problem, we need to understand the relationship between the rectangle and the resulting cylinder.

When the rectangle is rotated around its shorter side, the shorter side becomes the height of the cylinder, and the longer side becomes the circumference of the base of the cylinder.

Let's calculate the height, radius, and diameter of the cylinder step by step.

Height of the Cylinder

The height of the cylinder is equal to the length of the shorter side of the rectangle, which is 7 cm.

Height = 7 cm

Circumference of the Base of the Cylinder

The circumference of the base of the cylinder is equal to the length of the longer side of the rectangle, which is 8 cm.

Circumference = 8 cm

Radius of the Cylinder

The radius of the cylinder can be calculated using the formula:

Radius = Circumference / (2 * π)

Substituting the value of the circumference, we get:

Radius = 8 cm / (2 * π)

To get a decimal approximation, we can use the value of π as 3.14.

Radius ≈ 8 cm / (2 * 3.14)

Radius ≈ 1.27 cm

Diameter of the Cylinder

The diameter of the cylinder is twice the radius.

Diameter = 2 * Radius

Substituting the value of the radius, we get:

Diameter = 2 * 1.27 cm

Diameter ≈ 2.54 cm

Summary

To summarize, when a rectangle with sides measuring 8 cm and 7 cm is rotated around its shorter side, the resulting cylinder has the following dimensions: - Height: 7 cm - Radius: 1.27 cm - Diameter: 2.54 cm

Please let me know if you need any further clarification.