Question

Площадь осевого сечения равна 72 см² его образующая в 2 раза больше диаметра основания найти обьем цилиндра. пожалуйста напишите развернутый ответ

Answer 1

D*2D=72
2D²=72
D²=36
D=6
R=3
H=2D=12
V=πR²*H=π3²*12=108π
Ответ: 108π cм³ = 339.12 cм³

Answer 2

Sосевого сечения = h*2*r, h=4*r, Sосевого сечения = 8*r^2,
8*r^2=72, то r=3, 
Vцилиндра = pi*h*r^2=pi*4*r^3=3.14*4*27=339.12.

Answer 3

Calculation of Cylinder Volume

To find the volume of a cylinder, we need to know the area of the base and the height of the cylinder. In this case, we are given that the area of the base (A) is 72 cm² and the diameter of the base (d) is twice the radius (r) of the base.

Let's break down the steps to find the volume of the cylinder:

1. Find the radius (r) of the base: - Since the diameter (d) is twice the radius, we can divide the diameter by 2 to find the radius. - Let's assume the diameter of the base is x cm. Therefore, the radius (r) would be x/2 cm.

2. Calculate the height (h) of the cylinder: - The height of the cylinder is not given in the question, so we cannot determine it directly. We need more information to calculate the height.

3. Use the formula for the volume of a cylinder: - The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height. - Since we know the radius (r) and the area of the base (A), we can use the formula A = πr² to find the radius (r) and then substitute it into the volume formula.

Let's proceed with the calculations:

1. Find the radius (r) of the base: - We are given that the area of the base (A) is 72 cm². - Using the formula A = πr², we can solve for r: - 72 = πr² - Divide both sides of the equation by π: 72/π = r² - Take the square root of both sides to find r: √(72/π) = r - Therefore, the radius (r) of the base is approximately 4.82 cm.

2. Calculate the height (h) of the cylinder: - The height of the cylinder is not provided in the question, so we cannot determine it directly. We need more information to calculate the height.

3. Use the formula for the volume of a cylinder: - The formula for the volume of a cylinder is V = πr²h. - Substituting the known values, we have V = π(4.82)²h. - Since we don't have the height (h), we cannot calculate the volume of the cylinder without this information.

In conclusion, without the height of the cylinder, we cannot determine the volume. We need additional information to calculate the volume of the cylinder accurately.

Please provide the height of the cylinder so that we can calculate the volume for you.