Question

В основании прямой призмы лежит квадрат со стороной 3. Боковые ребра равны 7/П . Найдите объем цилиндра, описанного около этой призмы.

Answer 1

Объём цилиндра вычисляется по формуле V=П·R²H. Высота цилиндра равна длине бокового ребра, т.е. 7/П, квадрат радиуса основания цилиндра равен  квадрату половины диагонали основания призмы. Квадрат диагонали найдём по Т.Пифагора, как гипотенузу прямоугольного треугольника с катетами  равными сторонам квадрата, т.е. по 3. R²=(d/2)²=(3²+3²):4=4,5. Подставим найденные значения в формулу.

V=П·4,5·7/П=31,5

Answer 2

Calculating the Volume of a Cylinder Inscribed in a Prism

To find the volume of a cylinder inscribed in a prism, we can use the formula for the volume of a cylinder. Given that the base of the prism is a square with a side length of 3 and the lateral edges are equal to 7/π, we can proceed with the calculation.

Volume of the Cylinder

The volume of a cylinder can be calculated using the formula:

V = πr^2h

Where: - V = Volume - r = Radius of the cylinder - h = Height of the cylinder

Finding the Radius of the Cylinder

The radius of the cylinder inscribed in the prism is equal to half the side length of the base of the prism. Since the base of the prism is a square with a side length of 3, the radius of the inscribed cylinder is:

r = 3/2

Finding the Height of the Cylinder

The height of the cylinder is equal to the height of the prism. Since the lateral edges of the prism are equal to 7/π, the height of the prism is also 7/π.

h = 7/π

Calculating the Volume

Now, we can calculate the volume of the cylinder using the formula:

V = π * (3/2)^2 * (7/π)

Solving this equation will give us the volume of the cylinder inscribed in the given prism.

Let's calculate the volume.