Question

Найдите объем цилиндра вписанного в куб со стороной 2. В ответе укажите V/π

Answer 1

Цилиндр вписан в куб, => 
высота цилиндра Н=а ребру куба, H=2.
диаметр цилиндра d =а ребру куба
R=a/2. R=1

объём цилиндра:
V=S осн*Н
Sосн=πR²

V=πR²H
V=π*1² *2
V=2π
V/π=2π/2=2

ответ:  2

Answer 2

Calculating the Volume of a Cylinder Inscribed in a Cube

To find the volume of a cylinder inscribed in a cube, we need to determine the radius and height of the cylinder. Since the cube has a side length of 2, the diameter of the cylinder will be equal to the side length of the cube.

Let's calculate the volume step by step:

1. Find the radius of the cylinder: - The diameter of the cylinder is equal to the side length of the cube, which is 2. - The radius is half the diameter, so the radius of the cylinder is 1.

2. Find the height of the cylinder: - Since the cylinder is inscribed in the cube, its height will be equal to the side length of the cube, which is 2.

3. Calculate the volume of the cylinder: - The formula for the volume of a cylinder is V = πr^2h, where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius, and h is the height. - Substituting the values we found, the volume of the cylinder is V = π(1^2)(2) = 2π.

Therefore, the volume of the cylinder inscribed in the cube with a side length of 2 is 2π.