Question

Осевым сечением цилиндра является прямоугольник, стороны которого равны 3 см и 4 см. Найдите радиус отписанной сферы.

Answer 1

R=2,5 cм.................................

Answer 2

Finding the Radius of the Circumscribed Sphere

To find the radius of the circumscribed sphere of a cylinder, we need to use the properties of the cylinder's cross-section. In this case, the cross-section is a rectangle with sides measuring 3 cm and 4 cm.

The radius of the circumscribed sphere can be found using the formula:

Radius of the circumscribed sphere = (Diagonal of the rectangle) / 2

To find the diagonal of the rectangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (diagonal) of a right triangle is equal to the sum of the squares of the other two sides.

In this case, the diagonal of the rectangle is the hypotenuse of a right triangle with sides measuring 3 cm and 4 cm. Using the Pythagorean theorem, we can calculate the diagonal as follows:

Diagonal = √(3^2 + 4^2)

Let's calculate the diagonal and then find the radius of the circumscribed sphere.

Calculation:

Diagonal = √(3^2 + 4^2) = √(9 + 16) = √25 = 5 cm

Radius of the circumscribed sphere = Diagonal / 2 = 5 cm / 2 = 2.5 cm

Therefore, the radius of the circumscribed sphere is 2.5 cm.