Question

Круг радиуса 2,5 см перемещается по столу так , что его центр обходит контур квадрата со стороной 4 см.Чему равна площадь части стола, образованная следом круга, с точностью до 1 см³

Answer 1

Обозначим сторону квадрата a радиус R
Площадь следа будет равна: площадь квадрата, выписываемого центром круга + 4 прямоугольника, со сторонами квадрат х радиус+ 4 сектора в 1/4 площади круга (т.е. эти сектора на один круг потянут)

Просто рисуем след. И смотрим на какие простые фигуры его легче разбить. Я вижу так.

$S=a^2+4*(a*R)+\pi *R^2$
$S=16+4*(2,5*4)+3,1416*6,25 \approx 75,6 \approx 76$ см²

Answer 2

Calculation of the Area of the Circle's Path

To find the area of the part of the table formed by the path of the circle, we need to calculate the area of the square and subtract the area of the inscribed circle.

The radius of the circle is given as 2.5 cm, and the side length of the square is given as 4 cm.

Calculating the Area of the Square

The area of a square is calculated by squaring the length of one of its sides. In this case, the side length is 4 cm, so the area of the square is 16 cm².

Calculating the Area of the Circle

The area of a circle is calculated using the formula A = πr², where A is the area and r is the radius.

The radius of the circle is given as 2.5 cm, so the area of the circle is:

A = π(2.5 cm)²

To calculate the area, we need the value of π. The value of π is approximately 3.14159.

A ≈ 3.14159 * (2.5 cm)²

A ≈ 3.14159 * 6.25 cm²

A ≈ 19.63495 cm²

Therefore, the area of the circle is approximately 19.63495 cm².

Calculating the Area of the Part of the Table

To find the area of the part of the table formed by the path of the circle, we subtract the area of the circle from the area of the square.

Area of the part of the table = Area of the square - Area of the circle

Area of the part of the table ≈ 16 cm² - 19.63495 cm²

Area of the part of the table ≈ -3.63495 cm²

Since the area cannot be negative, we can conclude that the area of the part of the table formed by the path of the circle is approximately 0 cm².

Please note that the precision of the answer is given as 1 cm², so the final answer is rounded to the nearest whole number.