Question

50 баллов срочно!!! В кафе «Пицццццачка» ко дню Святого Валентина устроили акцию: две пиццы по цене одной. Правда, при этом, если одна пицца имела диаметр 40 см, то две другие (которые вместо одной), имели такой диаметр, чтобы суммарное количество продукта не превышало количество продукта в одной пицце. Какой наибольший натуральный диаметр этих пицц возможен, если толщина у всех одинаковая?

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

Problem Analysis

We are given that a cafe called "Пицццццачка" is offering a Valentine's Day promotion where two pizzas are sold for the price of one. However, there is a condition that if one pizza has a diameter of 40 cm, the combined amount of ingredients in the two additional pizzas should not exceed the amount in the original pizza. We need to determine the largest natural diameter possible for these pizzas, assuming the thickness is the same for all pizzas.

Solution

To solve this problem, we need to consider the total area of the pizzas. Since the thickness is the same for all pizzas, we can ignore it in our calculations.

Let's assume the diameter of the two additional pizzas is x cm. The area of the original pizza with a diameter of 40 cm is given by:

Area of original pizza = π * (40/2)^2 = 1600π cm^2

The area of the two additional pizzas is given by:

Area of two additional pizzas = 2 * (π * (x/2)^2) = 2π * (x/2)^2 = π * (x/2)^2

According to the problem statement, the combined amount of ingredients in the two additional pizzas should not exceed the amount in the original pizza. This means that the area of the two additional pizzas should be less than or equal to the area of the original pizza:

π * (x/2)^2 ≤ 1600π

Simplifying the inequality:

(x/2)^2 ≤ 1600

Taking the square root of both sides:

x/2 ≤ √1600

Simplifying further:

x/2 ≤ 40

Multiplying both sides by 2:

x ≤ 80

Therefore, the largest natural diameter possible for the two additional pizzas is 80 cm.

Conclusion

The largest natural diameter possible for the two additional pizzas in the "Пицццццачка" cafe's Valentine's Day promotion is 80 cm, assuming the thickness is the same for all pizzas.