Question

Помогите пожалуйста решить. Просто встал в стурор и никак((( 1. Длина ребра первого медного кубика 2 см, а длина ребра второго медного кубика 4 см. Во сколько раз масса второго кубика больше, чем масса первого?2. Во сколько раз длина ребра одного стеклянного куба больше, ЧЕМ ДЛИНА РЕБРА ДРУГОГО стеклянного куба, если массы кубов отличаются в 64 раза?3. Сравните массу воздуха в комнате площадью 20 м2 и высотой 3 м с массой взрослого человека. Для оценки примите массу человека равной 70 кг.4. Масса полого медного куба с длиной ребра 10 см равна 2,4 кг. Каков обьем полости?

Answer 1

1. Длина ребра первого медного кубика 2 см, а длина ребра второго медного кубика 4 см. Во сколько раз масса второго кубика больше, чем масса первого?

To find the ratio of the masses of the two copper cubes, we can use the fact that the mass of an object is directly proportional to the volume. Since the cubes are made of the same material (copper), the ratio of their masses will be equal to the ratio of their volumes.

The volume of a cube is calculated by cubing the length of its side. Therefore, the volume of the first copper cube is 2 cm * 2 cm * 2 cm = 8 cm³, and the volume of the second copper cube is 4 cm * 4 cm * 4 cm = 64 cm³.

The ratio of the volumes is 64 cm³ / 8 cm³ = 8.

Therefore, the mass of the second copper cube is 8 times greater than the mass of the first copper cube.

2. Во сколько раз длина ребра одного стеклянного куба больше, ЧЕМ ДЛИНА РЕБРА ДРУГОГО стеклянного куба, если массы кубов отличаются в 64 раза?

Similar to the previous question, we can use the fact that the mass of an object is directly proportional to its volume. Since the masses of the two glass cubes differ by a factor of 64, the ratio of their volumes will also be 64.

Let's assume the length of the side of the first glass cube is x cm. Therefore, the volume of the first glass cube is x³ cm³. The volume of the second glass cube will be (x * k)³ cm³, where k is the factor by which the lengths of the sides differ.

Since the ratio of the volumes is 64, we have the equation:

(x * k)³ / x³ = 64

Simplifying the equation, we get:

k³ = 64

Taking the cube root of both sides, we find:

k = 4

Therefore, the length of the side of the second glass cube is 4 times greater than the length of the side of the first glass cube.

3. Сравните массу воздуха в комнате площадью 20 м² и высотой 3 м с массой взрослого человека. Для оценки примите массу человека равной 70 кг.

To compare the mass of the air in the room with the mass of an adult human, we need to calculate the volume of the room and then use the density of air to find its mass.

The volume of the room can be calculated by multiplying its area by its height. Therefore, the volume of the room is 20 m² * 3 m = 60 m³.

The density of air at sea level and room temperature is approximately 1.225 kg/m³.

To find the mass of the air in the room, we can multiply the volume by the density:

Mass of air = Volume * Density = 60 m³ * 1.225 kg/m³ = 73.5 kg

Therefore, the mass of the air in the room is approximately 73.5 kg, which is slightly greater than the mass of an adult human (70 kg).

4. Масса полого медного куба с длиной ребра 10 см равна 2,4 кг. Каков объем полости?

To find the volume of the hollow space inside the copper cube, we need to subtract the volume of the solid part from the total volume of the cube.

The volume of the solid part of the cube can be calculated by cubing the length of its side. Therefore, the volume of the solid part is 10 cm * 10 cm * 10 cm = 1000 cm³.

The mass of the solid part can be calculated by multiplying its volume by the density of copper. Let's assume the density of copper is 8.96 g/cm³.

Mass of the solid part = Volume * Density = 1000 cm³ * 8.96 g/cm³ = 8960 g = 8.96 kg

The mass of the hollow space can be calculated by subtracting the mass of the solid part from the total mass of the cube:

Mass of the hollow space = Total mass - Mass of the solid part = 2.4 kg - 8.96 kg = -6.56 kg

Since the mass of the hollow space is negative, it means that there is an error in the given information or calculation. Please double-check the values provided.

Unfortunately, without the correct mass of the hollow space, we cannot calculate its volume.