Question

Плотность алюминия р=2.7 г/см3. Алюминевый куб с ребром 10 см имеет массу 2,43 кг. Есть ли полость внутри куба? Если есть, определите её объм

Answer 1

Vал.=m/р = 2430 / 2,7=900см^3
Vкуба=10^3=1000 cм^3
Vпол.=1000-900= 100 см^3
Ответ : есть, 100 см^3.

Answer 2

Calculation of the Aluminum Cube's Volume and Mass

To determine if there is a cavity inside the aluminum cube, we first need to calculate the volume and mass of the cube.

Given: - Density of aluminum (ρ) = 2.7 g/cm³ - Side length of the aluminum cube (a) = 10 cm - Mass of the aluminum cube (m) = 2.43 kg

To find the volume of the aluminum cube, we can use the formula:

Volume (V) = Side length (a)³

Substituting the given value of the side length, we have:

V = 10 cm * 10 cm * 10 cm = 1000 cm³

Next, we can convert the volume from cm³ to m³:

V = 1000 cm³ * (1 m / 100 cm)³ = 0.001 m³

Now, let's calculate the mass of the aluminum cube in grams:

Mass (m) = 2.43 kg * 1000 g/kg = 2430 g

Determining the Presence of a Cavity

To determine if there is a cavity inside the aluminum cube, we can compare the calculated mass of the cube with the expected mass based on the density and volume of solid aluminum.

The expected mass (m_expected) can be calculated using the formula:

m_expected = Density (ρ) * Volume (V)

Substituting the given values, we have:

m_expected = 2.7 g/cm³ * 0.001 m³ = 2.7 g

Comparing the calculated mass (2430 g) with the expected mass (2.7 g), we can conclude that there is indeed a cavity inside the aluminum cube. The difference in mass indicates the presence of a void or empty space within the cube.

Calculation of the Cavity Volume

To determine the volume of the cavity, we can subtract the volume of the solid aluminum from the total volume of the cube.

The volume of the cavity (V_cavity) can be calculated using the formula:

V_cavity = Total Volume (V) - Volume of Aluminum (V_aluminum)

Substituting the given values, we have:

V_cavity = 0.001 m³ - 0.001 m³ = 0 m³

Therefore, the volume of the cavity inside the aluminum cube is 0 cubic meters.

Please note that the calculations provided are based on the given information and assumptions.