Question

Сосуд имеет форму цилиндра, высота которого равна h см, а радиус основания r см, где 2 дм < h < 2,1 дм, 0, 5 дм < r < 0,6 дм. Зная, что объем цилиндра вычисляется по формуле V = πr2h и 3 < π < 3,1, оцени вместимость сосуда.

Answer 1

Ответ:

1,5дм 2,3436

Пошаговое объяснение:ответ правильный

Answer 2

Calculating the Volume of a Cylinder

To estimate the capacity of the vessel, we can use the formula for the volume of a cylinder, which is given by:

V = πr^2h

where: - V is the volume of the cylinder, - π is a mathematical constant approximately equal to 3.14, - r is the radius of the base of the cylinder, and - h is the height of the cylinder.

Based on the given information, we have: - The height of the cylinder, h, is between 2 dm and 2.1 dm (1 dm = 10 cm). - The radius of the base of the cylinder, r, is between 0.5 dm and 0.6 dm.

To estimate the capacity of the vessel, we need to calculate the volume using the given range of values for h and r.

Calculation

Let's calculate the volume of the cylinder using the minimum and maximum values for h and r:

1. Minimum values: - h = 2 dm = 20 cm - r = 0.5 dm = 5 cm

Substituting these values into the formula, we get: V_min = π * (5 cm)^2 * 20 cm

2. Maximum values: - h = 2.1 dm = 21 cm - r = 0.6 dm = 6 cm

Substituting these values into the formula, we get: V_max = π * (6 cm)^2 * 21 cm

Estimation

To estimate the capacity of the vessel, we can calculate the minimum and maximum volumes using the given range of values for h and r.

Using the approximate value of π as 3.14, we can calculate the estimated minimum and maximum volumes:

1. Minimum volume: V_min = 3.14 * (5 cm)^2 * 20 cm

2. Maximum volume: V_max = 3.14 * (6 cm)^2 * 21 cm

Please note that these calculations are estimates based on the given range of values for h and r.

Let me calculate the estimated minimum and maximum volumes for you.