Question

Найдите площадь круга и длину окружности если периметр вписанного в нее квадрата равна 48 см? помогите пожалуйста

Answer 1

P=48=4a4 => a4=R√2 =>r R=6√2 
S=πR^2=(6√2)^2π=72π
C=2πR=12√2π

Answer 2

Calculation of Circle Area and Circumference

To find the area and circumference of a circle, we need to know the perimeter of the square inscribed in it. In this case, the perimeter of the square is given as 48 cm.

Let's denote the side length of the square as s. The perimeter of the square is given by the formula:

Perimeter of Square = 4s

Since the perimeter of the square is 48 cm, we can set up the equation:

4s = 48

Now, let's solve for s:

s = 48 / 4 = 12 cm

The side length of the square is 12 cm.

Calculation of Circle Area

The diagonal of the square is equal to the diameter of the inscribed circle. The diagonal of a square can be calculated using the formula:

Diagonal of Square = s√2

Substituting the value of s into the formula, we get:

Diagonal of Square = 12√2 cm

Since the diagonal of the square is equal to the diameter of the circle, the diameter of the circle is also 12√2 cm.

The formula for the area of a circle is:

Area of Circle = πr^2

where r is the radius of the circle.

Since the diameter is twice the radius, we can calculate the radius using the formula:

Radius = Diameter / 2 = (12√2) / 2 = 6√2 cm

Now, substituting the value of the radius into the formula for the area of a circle, we get:

Area of Circle = π(6√2)^2 = 36π cm^2

Therefore, the area of the circle is 36π cm^2.

Calculation of Circle Circumference

The formula for the circumference of a circle is:

Circumference of Circle = 2πr

Substituting the value of the radius into the formula, we get:

Circumference of Circle = 2π(6√2) cm

Simplifying the expression, we have:

Circumference of Circle = 12π√2 cm

Therefore, the circumference of the circle is 12π√2 cm.

To summarize: - The area of the circle is 36π cm^2. - The circumference of the circle is 12π√2 cm.

Please let me know if there's anything else I can help you with!