Question

Мистеру Фоксу надо покрасить трубу на даче. Диаметр отверстия трубы равен 30 см, а толщина её стенок 1 см. Хватит ли 2 кг краски, чтобы покрасить снаружи 8 м этой трубы, если на 1 кв м её поверхности расходуется 200 г краски? хватит не хватит Сколько килограмм краски необходимо для покраски? Ответ округлите до десятых?

Answer 1

Ответ: 1. Хватит.

2. 1,6

Answer 2

Calculation of Paint Needed to Paint the Pipe

To determine whether 2 kg of paint is sufficient to paint the outside of an 8 m pipe with a diameter of 30 cm and wall thickness of 1 cm, we need to calculate the surface area of the pipe and the amount of paint required.

The surface area of a pipe can be calculated using the formula:

Surface Area = 2πrh + πr^2

Where: - r is the radius of the pipe (half of the diameter) - h is the height of the pipe (8 m in this case)

Let's calculate the surface area of the pipe:

1. Calculate the radius: - Diameter = 30 cm - Radius = Diameter / 2 = 30 cm / 2 = 15 cm = 0.15 m

2. Calculate the surface area of the pipe: - Surface Area = 2πrh + πr^2 - Surface Area = 2π(0.15 m)(8 m) + π(0.15 m)^2 - Surface Area = 2π(1.2 m^2) + π(0.0225 m^2) - Surface Area = 2.4π m^2 + 0.0707π m^2 - Surface Area ≈ 2.471π m^2

Now, let's calculate the amount of paint required:

1. Given that the paint consumption is 200 g per 1 square meter of surface area, we can calculate the total paint required: - Paint Required = Surface Area × Paint Consumption - Paint Required = 2.471π m^2 × 200 g/m^2 - Paint Required ≈ 494.2π g

2. Convert the paint required to kilograms: - Paint Required in kg = Paint Required / 1000 - Paint Required in kg ≈ 0.4942π kg

Therefore, approximately 0.4942π kg of paint is needed to paint the outside of the 8 m pipe.

Please note that the answer is rounded to the nearest tenth.