Question

В городе была сделана цветочная клумба, образованная из квадрата и четырёх полукругов. Площадь клумбы приблизительно равна 1960 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? м

Answer 1

6,2x^2+4x^2=49010,2x^2=490x^2=49 примерноx=v49=7 метров примерно длина радиуса полукругов2*7=14 метров сторона квадрата2*14*3,1=86,8 метра длина забора

Answer 2

Calculation of the Flower Bed

To find the length of the decorative fence required around the flower bed, we need to calculate the dimensions of the square and the semicircles that form the flower bed.

1. Length of the Square Side: - The flower bed is formed by a square and four semicircles. - Let's assume the side length of the square is x meters. - The area of the square is given as 1960 m². - The formula for the area of a square is A = side length × side length. - Therefore, we can write the equation as x × x = 1960. - Solving this equation, we find that the side length of the square is x = √1960 ≈ 44.27 meters.

2. Length of the Semicircle Radius: - Each semicircle forms half of a circle. - The formula for the area of a circle is A = π × r², where r is the radius. - Since we are given an approximate value of π as 3.1, we can use it for our calculations. - The area of one semicircle is equal to half the area of a full circle, so we can write the equation as (π × r²) / 2 = 1960. - Solving this equation, we find that the radius of each semicircle is r = √(2 × 1960 / π) ≈ 27.99 meters.

3. Length of the Decorative Fence: - The decorative fence consists of the four sides of the square and the circumference of each semicircle. - The formula for the circumference of a circle is C = 2 × π × r. - Since we have semicircles, we need to consider only half the circumference for each semicircle. - Therefore, the length of the decorative fence is equal to the sum of the four sides of the square and the circumferences of the four semicircles. - We can calculate it as follows: - Length of the square sides: 4 × x = 4 × 44.27 ≈ 177.08 meters - Length of the semicircle circumferences: 4 × (2 × π × r / 2) = 4 × (2 × 3.1 × 27.99 / 2) ≈ 175.43 meters - Total length of the decorative fence: 177.08 + 175.43 ≈ 352.51 meters

Therefore, approximately 352.51 meters of decorative fence are required around the flower bed.

Please note that the calculations are based on the assumption that the flower bed is a perfect square and the semicircles are perfectly aligned with the square.