Question

В городе была сделана цветочная клумба, образованная из квадрата и четырёх полукругов. Площадь клумбы приблизительно равна 90 м². Сколько метров декоративного забора необходимо вокруг клумбы? В расчётах использовано округлённое значение π≈3. 1. Какова длина стороны квадрата? м 2. Какова длина радиуса полукругов? м 3. Какова длина декоративного забора? мдаю девятнадцать баллов токо помогите

Answer 1

4 полукруга-это 2 круга
S круга=1/4$\pi$D²
S квадрата=D²
Sобщ=2S круга+S квадрата
90=2(1/4$\pi$D²)+D²
90=0.5$\pi$D²+D²
90=(0.5*3+1)*D²
D²=90:2.5=36
D=√36=6 м
так как D одновременно является стороной квадрата, то сторона квадрата равна 6 м
радиус полукругов R=D/2=6/2=3 м
длина забора-это длина окружности двух кругов
Lокр=$\pi$*D
Lокр=3*6=18 м
Lобщ=2Lокр=2*18=36 м
36 м-это длина забора и соответственно столько метров и надо.

Answer 2

Calculation of the Lengths

To determine the length of the sides of the square and the radius of the semicircles, we can use the given information that the total area of the flower bed is approximately 90 m².

Let's denote the side length of the square as x and the radius of the semicircles as r.

The area of the square is given by x^2, and the area of each semicircle is given by (1/2) * π * r^2. Since there are four semicircles, the total area of the semicircles is 4 * (1/2) * π * r^2.

The total area of the flower bed is the sum of the area of the square and the area of the semicircles:

x^2 + 4 * (1/2) * π * r^2 = 90

Now, let's solve this equation to find the values of x and r.

Solving the Equation

To solve the equation, we need to make some assumptions. Since the value of π is approximated as 3.1, we will use this approximation in our calculations.

1. Finding the length of the side of the square (x):

Rearranging the equation, we have:

x^2 = 90 - 4 * (1/2) * 3.1 * r^2

Simplifying further:

x^2 = 90 - 6.2 * r^2

Taking the square root of both sides:

x = √(90 - 6.2 * r^2)

2. Finding the length of the radius of the semicircles (r):

Rearranging the equation, we have:

r^2 = (90 - x^2) / (4 * (1/2) * 3.1)

Simplifying further:

r^2 = (90 - x^2) / 6.2

Taking the square root of both sides:

r = √((90 - x^2) / 6.2)

Calculating the Length of the Decorative Fence

To calculate the length of the decorative fence required around the flower bed, we need to consider the perimeter of the square and the circumference of the semicircles.

1. Perimeter of the square:

The perimeter of a square is given by 4 * x.

2. Circumference of the semicircles:

The circumference of a semicircle is given by π * r + 2 * r (half the circumference of a full circle plus the diameter).

Since there are four semicircles, the total circumference of the semicircles is 4 * (π * r + 2 * r).

3. Total length of the decorative fence:

The total length of the decorative fence is the sum of the perimeter of the square and the circumference of the semicircles:

Total length = 4 * x + 4 * (π * r + 2 * r)

Now, let's substitute the values of x and r that we calculated earlier into this equation to find the total length of the decorative fence.

Calculation Results

Using the given approximation of π as 3.1, we can calculate the lengths:

1. Length of the side of the square (x): - x = √(90 - 6.2 * r^2)

2. Length of the radius of the semicircles (r): - r = √((90 - x^2) / 6.2)

3. Total length of the decorative fence: - Total length = 4 * x + 4 * (π * r + 2 * r)

Please provide the value of r so that we can calculate the lengths and the total length of the decorative fence.