Question

Осьовим перерізом циліндра є квадрат із діагоналлю 6коренів з 12 см.. Чому дорівнює обєм циліндра?

Answer 1

по моему такая формула V=pi *R^2*H

Answer 2

Calculating the Volume of the Cylinder with a Square Cross-Section

To calculate the volume of a cylinder with a square cross-section, we can use the formula:

Volume = Area of the base × Height

First, let's find the area of the base, which is the area of the square.

The diagonal of the square is given as 6√2 cm, which is equal to 12 cm. We can use this information to find the side length of the square.

Finding the Side Length of the Square

The formula to find the side length of a square from the diagonal is:

Side length = Diagonal / √2

Substituting the given value of the diagonal:

Side length = 12 / √2 = 6√2 / 2 = 3√2 cm

Now that we have the side length of the square, we can find the area of the base.

Calculating the Area of the Base

The formula to find the area of a square is:

Area = Side length × Side length

Substituting the value of the side length:

Area = 3√2 × 3√2 = 9 × 2 = 18 cm²

Now that we have the area of the base, we can proceed to calculate the volume of the cylinder.

Calculating the Volume

The volume of the cylinder is given by the formula:

Volume = Area of the base × Height

We don't have the height of the cylinder provided in the question, so we cannot calculate the exact volume without that information. If the height of the cylinder is provided, we can use the formula to calculate the volume.

If you have the height of the cylinder, please provide it, and I can help you calculate the volume using the given information.