Question

Сторони прямокутника = 30см. і 40см. Знайдіть площу круга описаного навколо цього прямокутника

Answer 1

Найдём диагональ прямоугольника, она же будет диаметром круга. По т.Пифагора √(30²+40²)=50. Это диаметр, радиус будет равен половине, т.е. 25. Sкруга=πr²=π25²=625.
Ответ:625.

Answer 2

Finding the Area of a Circle Inscribed Around a Rectangle

To find the area of a circle inscribed around a rectangle, we need to know the dimensions of the rectangle. In this case, the rectangle has sides measuring 30 cm and 40 cm.

The formula for finding the area of a circle is:

Area of a Circle = π * r^2

To find the radius of the circle, we can use the diagonal of the rectangle, which is also the diameter of the circle. The diagonal can be found using the Pythagorean theorem:

Diagonal = √(Length^2 + Width^2)

Let's calculate the diagonal of the rectangle:

Diagonal = √(30^2 + 40^2) = √(900 + 1600) = √2500 = 50 cm

Now, we can find the radius of the circle by dividing the diameter (which is the diagonal) by 2:

Radius = Diagonal / 2 = 50 cm / 2 = 25 cm

Finally, we can calculate the area of the circle using the formula mentioned earlier:

Area of the Circle = π * (25 cm)^2

To find the value of π, we can use an approximation of 3.14.

Area of the Circle = 3.14 * (25 cm)^2

Calculating the area:

Area of the Circle = 3.14 * (25 cm)^2 = 3.14 * 625 cm^2 = 1962.5 cm^2

Therefore, the area of the circle inscribed around the given rectangle is 1962.5 cm^2.

Please note that the calculations provided are based on the given dimensions of the rectangle and the assumption that the circle is inscribed perfectly within the rectangle.