Question

Сколько потребуется подвод для перевозки стога сена, имеющего форму цилиндра с коническим верхом, если диаметр основания 6 м, высота стога 5м, причём высота конической части в 1.5 раза больше высоты цилиндрической части. Плотность Сеня 30кг/м3. На подводку можно погрузить 600 кг

Answer 1

1. Высота цилиндрической части    
Нц = Нстога/(1,5+1) = 5/(1,5+1) = 5/2,5 = 2 м
2 Высота конической части    Нк = Нстога -Нц = 5-2 = 3 м
3 Объем цилиндрической части
Vц = (π×dо²)×Hц/4 = (3,14×6²×2)/4 = 56,52 м³
4 Объем конусной части
Vк = (π×do²×Hк)/(3×4) = (3,14×6²×3)/(3×4) = 28,26 м³
5. Масса сена 
Мс = (Vц+Vк)×Δс = (56,52+28,26)×30 = 2543,4 кг
6 Необходимое количество подвод 
N = Мс/Рп = 2543,4/600 = 4,24 подводы = 5 подвод.
Ответ. Необходимо 5 подвод.
do - диаметр основания, м
Δс - плотность сена, кг/м³
Рп - грузоподъемность подводы, кг

Answer 2

Calculation of the Volume of the Haystack

To calculate the volume of the haystack, we need to find the volume of the cylindrical part and the volume of the conical part separately, and then add them together.

The volume of a cylinder is given by the formula: V_cylinder = π * r^2 * h_cylinder,

where r is the radius of the base (half of the diameter) and h_cylinder is the height of the cylindrical part.

The volume of a cone is given by the formula: V_cone = (1/3) * π * r^2 * h_cone,

where r is the radius of the base (half of the diameter) and h_cone is the height of the conical part.

In this case, the diameter of the base is 6 meters, so the radius is 3 meters. The height of the cylindrical part is 5 meters, and the height of the conical part is 1.5 times the height of the cylindrical part, which is 7.5 meters.

Let's calculate the volume of the cylindrical part: V_cylinder = π * 3^2 * 5 = 45π cubic meters.

And the volume of the conical part: V_cone = (1/3) * π * 3^2 * 7.5 = 22.5π cubic meters.

Adding the volumes together, we get the total volume of the haystack: V_total = V_cylinder + V_cone = 45π + 22.5π = 67.5π cubic meters.

Calculation of the Mass of the Haystack

To calculate the mass of the haystack, we need to multiply the volume by the density of the hay.

The density of the hay is given as 30 kg/m^3.

Let's calculate the mass of the haystack: Mass = V_total * Density = 67.5π * 30 kg.

Calculation of the Number of Trips Required for Transport

The maximum load capacity of the barge is given as 600 kg.

To calculate the number of trips required for transport, we need to divide the mass of the haystack by the maximum load capacity of the barge.

Let's calculate the number of trips required: Number of Trips = Mass / Maximum Load Capacity = (67.5π * 30) / 600.

Now, let's calculate the result:

Number of Trips = (67.5π * 30) / 600 ≈ 3.375π.

Therefore, approximately 3.375π trips will be required to transport the haystack.

Please note that the value of π is approximately 3.14159.