Question

В городе была сделана цветочная клумба, состоящая из квадрата и четырёх полукругов. Площадь клумбы приблизительно равна 40 м². Сколько метров декоративного забора необходимо вокруг клумбы? В расчётах использовано округлённое значение π≈3. 1. Какова длина стороны квадрата? 2. Какова длина радиуса полукругов? 3. Какова длина декоративного забора?

Answer 1

1. 20 м в кв.
2.r=20м в кв.
3.П×r в кв.=3×20в кв.=1320м в кв.=1320÷2=660×4=2640 м в кв.

Answer 2

Calculation of the Lengths

To find the lengths required for the flower bed and the decorative fence, we need to calculate the length of the square side and the radius of the semicircles.

1. Length of the Square Side: - Let's assume the length of the square side is x meters. - The area of the square is given as approximately 40 m². - The formula for the area of a square is Area = side × side. - Therefore, we can write the equation as x × x = 40. - Solving this equation, we find that x = √40 ≈ 6.32 meters.

2. Length of the Radius of the Semicircles: - The semicircles are formed by dividing the square into four equal parts. - Each semicircle is formed by taking the diameter as the side length of the square. - Therefore, the radius of each semicircle is half the side length of the square. - Hence, the radius of each semicircle is 6.32 / 2 = 3.16 meters.

Calculation of the Decorative Fence Length

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 the formula Perimeter = 4 × side. - Substituting the value of the side length, we get Perimeter = 4 × 6.32 = 25.28 meters.

2. Circumference of the Semicircles: - The circumference of a semicircle is given by the formula Circumference = π × radius. - Since we are using an approximate value of π as 3.1, the circumference of each semicircle is 3.1 × 3.16 = 9.796 meters. - As there are four semicircles, the total circumference of the semicircles is 4 × 9.796 = 39.184 meters.

3. Total Length of the Decorative Fence: - To find the total length of the decorative fence, we add the perimeter of the square and the circumference of the semicircles. - Therefore, the total length of the decorative fence required around the flower bed is 25.28 + 39.184 = 64.464 meters.

So, approximately 64.464 meters of decorative fence is needed 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 evenly divided.