the weight of three castings are 45.302kg 44.982kg and 45.716kg find the average weight if the 4th casting is taken the average weight becomes 46kg what is the weight of the 4th casting​

Answer:

Explanation:

The speed in the medium is always slower than the speed in a vacuum.

Answer:

The frequency of light can be calculated using the formula:

`c = λv`

Where `c` is the speed of light in a vacuum, `λ` is the wavelength of light, and `v` is the frequency of light.

The speed of light in a vacuum is `3.00 × 10^8 m/s`.

To convert the wavelength from nanometers to meters, we need to divide by `1 × 10^9`.

Thus, the frequency of light with a wavelength of 655 nm is:

`v = c/λ`

`v = (3.00 × 10^8 m/s)/(655 × 10^-9 m)`

`v = 4.58 × 10^14 Hz`

Therefore, the frequency of light with a wavelength of 655 nm is `4.58 × 10^14 Hz`.

Similarly, the frequency of light with a wavelength of 515 nm is:

`v = c/λ`

`v = (3.00 × 10^8 m/s)/(515 × 10^-9 m)`

`v = 5.83 × 10^14 Hz`

Therefore, the frequency of light with a wavelength of 515 nm is `5.83 × 10^14 Hz`.

Finally, the frequency of light with a wavelength of 475 nm is:

`v = c/λ`

`v = (3.00 × 10^8 m/s)/(475 × 10^-9 m)`

`v = 6.32 × 10^14 Hz`

Therefore, the frequency of light with a wavelength of 475 nm is `6.32 × 10^14 Hz`.

So, the frequency of light with a wavelength of 655 nm is `4.58 × 10^14 Hz`, the frequency of light with a wavelength of 515 nm is `5.83 × 10^14 Hz` and the frequency of light with a wavelength of 475 nm is `6.32 × 10^14 Hz`.

a) The total surface area of tin G in terms of π is 170π cm².

b) The mass of tin H is 336 g.

To solve the given problem, we need to determine the total surface area of tin G in terms of π and the mass of tin H. Since the mass of an empty cylindrical tin is proportional to its surface area, we can use the given information to find the solutions.

a) Total surface area of tin G in terms of π:

The surface area of a cylinder consists of two circular bases and the lateral surface area. The formula for the lateral surface area of a cylinder is given by:

Lateral surface area = 2πrh

where r is the radius of the base and h is the height of the cylinder.

In the case of tin G, the given dimensions are a radius of 5 cm and a height of 12 cm. Substituting these values into the formula, we can calculate the lateral surface area:

Lateral surface area = 2π(5 cm)(12 cm)

Lateral surface area = 120π cm²

Since the total surface area of the cylinder includes the two circular bases as well, we need to add their areas. The area of a circle is given by:

Area of a circle = πr²

The radius of the circular base of tin G is 5 cm, so the area of each circular base is:

Area of each circular base = π(5 cm)²

Area of each circular base = 25π cm²

To find the total surface area of tin G, we sum the lateral surface area and the areas of the two circular bases:

Total surface area of tin G = Lateral surface area + 2 × Area of each circular base

Total surface area of tin G = 120π cm² + 2 × 25π cm²

Total surface area of tin G = 120π cm² + 50π cm²

Total surface area of tin G = 170π cm²

Therefore, the total surface area of tin G in terms of π is 170π cm².

b) Mass of tin H:

We are given that the surface area of tin H is 792π cm². We can assume that the same proportionality factor applies as in tin G, so we can set up the following proportion:

(surface area of tin G) / (mass of tin G) = (surface area of tin H) / (mass of tin H)

Using the given values, we have:

(170π cm²) / (72 g) = (792π cm²) / (mass of tin H)

Cross-multiplying and solving for the mass of tin H, we get:

(170π cm²) × (mass of tin H) = (72 g) × (792π cm²)

mass of tin H = (72 g) × (792π cm²) / (170π cm²)

mass of tin H = 336 g

Therefore, the mass of tin H is 336 g.

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From the question;

1) It takes 15.75 years to decrease to 1/8

2) It takes 8.36 years to decrease to 1/3

Half-life is the length of time it takes for a chemical to degrade or go through a particular process. It frequently refers to the length of time it takes for half of a radioactive substance to decay into a stable form in the context of radioactive decay.

We know that;

[tex]N/No = (1/2)^t/t1/2[/tex]

No = initial amount

N = amount at time t

t = Time taken

t1/2 = half life

[tex]1/8 = (1/2)^t/5.252^-3 = 2^-t/5.25[/tex]

t = 15.75 years

Again;

[tex]1/3 = (1/2)^t/5.25[/tex]

ln0.33 = t/5.25ln0.5

t = ln0.33/ln0.5 * 5.25

t = 8.36 years

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The equivalent ratio in higher terms to eliminate decimals from the ratio 3.04 to 6 is 76 to 150.

To eliminate decimals from the ratio 3.04 to 6, we can multiply both terms of the ratio by a common factor that will result in whole numbers.

First, let's convert 3.04 to a fraction:

3.04 = 3 + 0.04 = 3 + 4/100 = 3 + 1/25 = 75/25 + 4/100 = 76/25

Now, the ratio 3.04 to 6 can be written as:

3.04/6 = 76/25 / 6

To eliminate the decimal, we can multiply both the numerator and denominator by 25:

(76/25) * 25 / (6 * 25) = 76 / 150

Therefore, the equivalent ratio in higher terms to eliminate decimals from the ratio 3.04 to 6 is 76 to 150.

By multiplying both terms by 25, we effectively scale up the ratio to eliminate the decimal and create whole numbers. This allows us to express the ratio in higher terms without decimals. The final ratio 76 to 150 represents the same relationship as the original ratio 3.04 to 6, but in whole number form.

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The average velocity of the car is 100 kilometers/hour south. This means that, on average, the car is traveling 100 kilometers per hour in the south direction relative to its starting point.

To determine the average velocity of the car, we need to calculate the displacement and divide it by the time taken. Velocity is defined as the rate of change of displacement with respect to time.

In this case, the car is traveling south, and its displacement is 200 kilometers from its starting point after 2 hours.

The average velocity is given by the formula:

Average velocity = Displacement / Time

The displacement is 200 kilometers south, and the time is 2 hours. Therefore, we have:

Average velocity = 200 kilometers south / 2 hours

Simplifying the calculation:

Average velocity = 100 kilometers/hour south

Hence, the correct answer is B. 100 kilometers/hour south. This indicates that the car's average velocity is 100 kilometers per hour towards the south direction.

It's important to note that velocity is a vector quantity and includes both magnitude (speed) and direction. In this case, the direction is specified as south, which indicates that the car is moving towards the south relative to its starting point.

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The following is an example of a surface wave option D. A wave on the surface of a drum that has been struck.

A surface wave is a type of wave that propagates along the interface between two different mediums, such as a solid and a fluid. It occurs specifically at the boundary between the two mediums. In the given options, a wave on the surface of a drum that has been struck best represents a surface wave.

Option OA describes a transverse wave traveling down a long, stretched string, which does not involve a boundary between different mediums.

Option OB describes a wave of ocean water as it reaches the beach, which is a combination of both transverse and longitudinal waves, but not specifically a surface wave.

Option OC describes a wave traveling down a stretched Slinky toy, which is similar to the wave on a long, stretched string and does not involve a boundary between different mediums.

Option OD describes a wave on the surface of a drum, which occurs at the boundary between the solid surface of the drum and the surrounding air. This wave represents a surface wave.

Therefore, option OD, a wave on the surface of a drum that has been struck, is an example of a surface wave.

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(a) The magnitude of the spring's displacement when the acceleration of the box is zero can be determined by equating the initial gravitational potential energy to the elastic potential energy stored in the spring.

(b) The magnitude of the spring's displacement when the spring is fully compressed can be determined by equating the initial gravitational potential energy to the elastic potential energy stored in the spring.

(a) To determine the magnitude of the spring's displacement when the acceleration of the box is zero, we need to apply the principles of conservation of energy.

Initially, the box has gravitational potential energy given by mgh, where m is the mass of the box, g is the acceleration due to gravity, and h is the height from which the box was dropped. The initial gravitational potential energy is converted into the elastic potential energy stored in the compressed spring and the kinetic energy of the box just before it makes contact with the spring.

The gravitational potential energy is given by:

mgh = (1.9 kg)[tex](9.8 m/s^2)h[/tex]

The elastic potential energy stored in the spring is given by:

1/2 kx^2[tex]kx^2[/tex], where k is the spring constant and x is the displacement of the spring.

The kinetic energy of the box just before it makes contact with the spring is given by:

[tex]1/2 mv^2,[/tex] where m is the mass of the box and v is the speed of the box.

Since the acceleration of the box is zero at the instant when the spring's displacement is maximum, the kinetic energy is zero. Therefore, we can equate the initial gravitational potential energy to the elastic potential energy to find the spring's displacement.

mgh = 1/2 [tex]kx^2[/tex]

Substituting the given values, we have:

[tex](1.9 kg)(9.8 m/s^2)h = 1/2 (300 N/m)x^2[/tex]

Solving for x, the magnitude of the spring's displacement, we can determine its value at the instant when the acceleration is zero.

(b) To find the magnitude of the spring's displacement when the spring is fully compressed, we need to consider the conservation of mechanical energy once again.

At maximum compression, all the initial gravitational potential energy is converted into the elastic potential energy stored in the compressed spring.

mgh = 1/2 [tex]kx^2[/tex]

Substituting the given values and solving for x, the magnitude of the spring's displacement, we can determine its value when the spring is fully compressed.

It's important to note that in both cases, the negative sign of the displacement indicates that the spring is being compressed. The magnitude of the displacement will be a positive value.

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Answer: P=30W

Explanation:

formula is p=w/t

p = power

w = work

t = elapsed time

input variables, solve then simplify.

The power of a lift that transfers 450 J of energy in 15 seconds is 30 watts.

Power is defined as the rate of doing work, i.e. the amount of work done per unit time.

Mathematically, it can be represented as follows:

Power = Work done / time taken

Therefore, the power of a lift that transfers 450 J of energy in 15 seconds can be calculated as follows:

Power = Work done / time taken= 450 J / 15 s= 30 W

Therefore, the power of the lift is 30 watts.

To explain further, we know that power is measured in watts (W), and it is the rate at which work is done or energy is transferred.

Here, we are given that the lift transfers 450 J of energy in 15 seconds.

We can find the power of the lift by dividing the amount of work done by the time taken to do it. By substituting the given values, we get the power of the lift as 30 W.

In simple terms, this means that the lift can transfer energy at a rate of 30 joules per second. This can also be interpreted as the lift can do 30 joules of work in one second.

Hence, we can conclude that the power of the lift is 30 watts.

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The distance between the two objects is reduced in half, that will be the changed force of attraction between them is option (E) 2.5 newtons.

According to Newton's law of universal gravitation, the force of attraction between two objects is inversely proportional to the square of the distance between them.

If the distance between Object A and Object B is reduced to half, the force of attraction will increase by a factor of 2² = 4. This means that the new force of attraction will be one-fourth of the original force.

Given that the original force of attraction is 5 newtons, the changed force of attraction between Object A and Object B, when the distance is reduced in half, will be 5 newtons / 4 = 1.25 newtons, which can be rounded to 2.5 newtons.The correct answer is option e.

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(a) When m₂ is released, its acceleration will be approximately -3.27 m/s².

(b) The tension in the string is approximately -13.08 N.

To determine the acceleration of m₂ when it is released and the tension in the string, we need to consider the forces acting on the system.

(a) Acceleration of m₂:

Since the pulley is assumed to be frictionless, the tension in the string is the same on both sides of the pulley. We can consider the system consisting of m₁ and m₂ as one body. The net force acting on this system is the difference between the weight of m₁ and the weight of m₂:

Net force = m₁g - m₂g

Applying Newton's second law, F = ma, where F is the net force and a is the acceleration, we have:

m₁g - m₂g = (m₁ + m₂)a

Rearranging the equation to solve for the acceleration, we get:

a = (m₁g - m₂g) / (m₁ + m₂)

Substituting the given values, m₁ = 2.00 kg and m₂ = 4.00 kg, and the acceleration due to gravity, g = 9.8 m/s², we can calculate the acceleration:

a = ((2.00 kg)(9.8 m/s²) - (4.00 kg)(9.8 m/s²)) / (2.00 kg + 4.00 kg)

a = (19.6 N - 39.2 N) / 6.00 kg

a = -19.6 N / 6.00 kg

a = -3.27 m/s²

Therefore, when m₂ is released, its acceleration will be approximately -3.27 m/s². The negative sign indicates that the acceleration is in the opposite direction of the gravitational force.

(b) Tension in the string:

The tension in the string can be determined by considering the forces acting on m₂. The net force on m₂ is equal to its mass multiplied by its acceleration:

Net force = m₂a

Substituting the given values, m₂ = 4.00 kg and a = -3.27 m/s², we can calculate the tension:

Tension = (4.00 kg)(-3.27 m/s²)

Tension = -13.08 N

Therefore, the tension in the string is approximately -13.08 N. The negative sign indicates that the tension acts in the opposite direction of the weight of m₂.

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The pressure in the tank at the new temperature of -65°C is approximately 554,666.67 Pa.

The given initial temperature is 27°C, and the initial pressure is 800,000 Pa. After reducing the temperature to -65°C,

We need to find the pressure of the Nitrogen gas.

Since the volume of the container is fixed,

We can use the combined gas law:

PV/T = constant

We know that the initial pressure (P1) is 800,000 Pa and the initial temperature (T1) is

27°C = 300 K. Let P2 be the pressure at -65°C = 208 K.

We can solve for P2 as follows:

P1/T1 = P2/T2Therefore, P2 = P1(T2/T1) = 800,000 (208/300)Pa= 554,666.67 Pa (rounded off to 3 decimal places)

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Answer:

The boiling point of nitrogen on the absolute temperature scale is 77.15 K

Explanation:

Temperature in Kelvin(Absolute temperature) = Temperature in Celcius + 273.15.

A rope pulls a Tesla out of mud. The guy pulls a force F⊥ of 300N, and theta = 4.2°. The tension force T is 298.44__ Newton.

The problem describes a Tesla that is stuck in the mud and needs to be pulled out using a rope. the guy pulls a force F⊥ of 300N and that the angle between the rope and the horizontal plane is θ = 4.2°. The goal is to find the tension force T exerted by the rope.To solve for T, we'll need to use trigonometry. We can break the force vector into its horizontal and vertical components as follows:

Fx = F⊥ cosθ and Fy = F⊥ sinθ.

Since the rope is pulling the Tesla horizontally, the horizontal component of the force will be the tension force T. So we have:

T = Fx = F⊥ cosθ = (300 N) cos(4.2°) ≈ 298.44 N

Taking the cosine of the angle is necessary since it's the adjacent side that we're interested in, which is the horizontal component of the force. Therefore, the tension force exerted by the rope is approximately 298.44 N.

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Answer:

which on a is the question

Answer:

Explanation:

A) The mass of the block is 33.3 Kg.

We know that F=ma

m=F/a

Where,

F⇒Force

m⇒mass

a⇒acceleration

Given,

F=100N

a=3m/s^2

m=100/3

m= 33.3Kg.

Therefore the mass of the block is 33.3 kg.

B) Distance traveled in 10s is 150m.

According to Newton's laws of motion,

s=ut+1/2at^2

s⇒displacement

u⇒initial velocity

t⇒time

Given,

u=0

t=10s

a=3m/s^2

s=0+1/2*3*100

s=150m.

Therefore distance traveled by the block after 10s is 150m.

C)The speed of the block after 10s will be 30m/s.

We know that

v^2=u^2+2as

v⇒Final velocity

u⇒initial velocity

v^2=0+2*3*150

v^2=900

v=30m/s.

Therefore the velocity of the block will be 30m/s after 10s.

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The resulting net electrical charge of the materials in this system is C: The net electrical charge remains neutral as electrons are transferred from one material to the other.

When two neutral materials are rubbed together, friction can cause the transfer of electrons from one material to another. Electrons, which carry a negative charge, can move from one material to the other during this process. However, it is important to note that the total number of electrons in the system remains the same.

Since electrons are transferred from one material to the other, the material that gains electrons becomes negatively charged, and the material that loses electrons becomes positively charged. These charges balance each other out, resulting in a neutral net electrical charge for the overall system.

Therefore, the net electrical charge of the materials in this system remains neutral, even though there is a transfer of electrons between them. Therefore, Option C is correct.

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The first harmonic of the standing wave on a string with a loose end represents half a wavelength.

The fraction of a wavelength represented by the first harmonic is 1/2.

The higher harmonics of a standing wave on a string with a loose end are odd-number multiples of the first harmonic.

1. The first harmonic of a standing wave on a string with a loose end occurs when there is a node near the driver end and an antinode at the loose end. To measure the frequency of the first harmonic, we need to determine the fraction of a wavelength represented by this standing wave.

The first harmonic of the standing wave on a string with a loose end represents half a wavelength.

The first harmonic of a standing wave on a string with a loose end consists of a node near the driver end and an antinode at the loose end. This configuration creates the simplest standing wave pattern.

In a standing wave, a node is a point where the amplitude of the wave is always zero, representing a point of minimum displacement. An antinode, on the other hand, is a point of maximum displacement, where the amplitude is at its highest.

Since the loose end does not invert the phase of the wave upon reflection, the reflected wave and the original wave constructively interfere at the loose end, resulting in an antinode.

In the first harmonic, there is exactly half a wavelength between the node near the driver end and the antinode at the loose end.

Therefore, the fraction of a wavelength represented by the first harmonic is 1/2.

2. To predict the frequencies of higher harmonics, we can use the relationship that the frequency of each harmonic is a multiple of the frequency of the first harmonic. The higher harmonics can be calculated as follows:

Second Harmonic: The second harmonic consists of two nodes and one additional antinode compared to the first harmonic. The fraction of a wavelength for the second harmonic is 1/2 * 2 = 1. Thus, the second harmonic has a frequency that is twice that of the first harmonic.

Third Harmonic: The third harmonic consists of three nodes and two additional antinodes compared to the first harmonic. The fraction of a wavelength for the third harmonic is 1/2 * 3 = 1.5. Thus, the third harmonic has a frequency that is three times that of the first harmonic.

Fourth Harmonic: The fourth harmonic consists of four nodes and three additional antinodes compared to the first harmonic. The fraction of a wavelength for the fourth harmonic is 1/2 * 4 = 2. Thus, the fourth harmonic has a frequency that is four times that of the first harmonic.

In general, the higher harmonics of a standing wave on a string with a loose end are odd-number multiples of the first harmonic.

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The statement that must be true is:  (Area of 1) + (Area of 2) = (Area of 3). This statement accurately reflects the relationship between the areas of the squares in the given diagram.

The correct answer is option B.

To determine which statement about the squares must be true, let's analyze the given diagram and the properties of squares.

In the diagram, square 1 is constructed on one side of the right triangle, square 2 is constructed on another side of the right triangle, and square 3 is constructed on the hypotenuse of the right triangle.

Statement A: (Perimeter of 1) + (Perimeter of 2) = (Area of 3)

This statement relates to the perimeters of squares 1 and 2 being equal to the area of square 3. However, this is not necessarily true. The perimeters of squares 1 and 2 are related to the lengths of their sides, while the area of square 3 is related to the length of its side. The perimeters and areas are different measures, so this statement is not necessarily true.

Statement B: (Area of 1) + (Area of 2) = (Area of 3)

This statement compares the areas of squares 1 and 2 to the area of square 3. Since squares have all sides equal in length, the areas of squares 1 and 2 are equal to the area of square 3. Therefore, this statement must be true

Statement C: (Perimeter of 1) + (Perimeter of 2) = (Perimeter of 3)

This statement relates to the perimeters of squares 1 and 2 being equal to the perimeter of square 3. However, since the squares have different side lengths, their perimeters are different. Therefore, this statement is not necessarily true.

Statement D: (Area of 1) + (Area of 2) = (Perimeter of 3)

This statement compares the areas of squares 1 and 2 to the perimeter of square 3. As mentioned earlier, the areas of squares 1 and 2 are equal to the area of square 3, which means they are not necessarily equal to the perimeter of square 3. Hence, this statement is not necessarily true.

Therefore, the correct statement is option B.

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The pattern of lines of force around two positive charges separated from each other demonstrates the repulsive nature of like charges and the direction and strength of the electric field between them.

When two positive charges are separated from each other, the lines of force (also known as electric field lines) originate from one positive charge and terminate on the other positive charge. The lines of force follow a pattern that reflects the repulsion between the positive charges.

Here's a verbal description of the pattern:

From each positive charge, the lines of force radiate outward in all directions.

The lines of force are evenly spaced and radially symmetric around each charge, indicating that the electric field strength is the same at all points along a given line.

As the lines of force move away from each charge, they curve away from each other, reflecting the repulsion between the positive charges.

The density of lines of force is higher near the charges and decreases as they move further apart.

The lines of force never cross each other, maintaining their continuous and unbroken nature.

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The frequency of light with a wavelength of 655 nm is[tex]4.57 x 10^14 Hz[/tex] and 515 nm is [tex]5.82 x 10^14[/tex] Hz and  475 nm is[tex]6.31 x 10^14 Hz[/tex]

The equation that links the speed of light to wavelength and frequency is

c = λν

Where, c = speed of lightλ = wavelengthν = frequency c is a constant of 2.998 x 10^8 m/s.

Calculating the frequency of light with a wavelength of

655 nm:λ = 655 nm = [tex]6.55 x 10^-7m[/tex]

Using the above equation, we get

c = λνν = c/λ = [tex](2.998 x 10^8 m/s)/(6.55 x 10^-7m)ν = 4.57 x 10^14 Hz[/tex]

Therefore, the frequency of light with a wavelength of 655 nm is 4.57 x [tex]10^14 Hz.[/tex]

Calculating the frequency of light with a wavelength of 515 nm:λ = 515 nm = [tex]5.15 x 10^-7m[/tex]

Using the above equation, we get

c = λνν = c/λ =[tex](2.998 x 10^8 m/s)/(5.15 x 10^-7m)ν = 5.82 x 10^14 Hz[/tex]

Therefore, the frequency of light with a wavelength of 515 nm is 5.82 x [tex]10^14 Hz[/tex].

Calculating the frequency of light with a wavelength of 475 nm:λ = 475 nm = [tex]4.75 x 10^-7[/tex]m Using the above equation, we get

c = λνν = c/λ = [tex](2.998 x 10^8 m/s)/(4.75 x 10^-7m)ν = 6.31 x 10^14 Hz[/tex]

Therefore, the frequency of light with a wavelength of 475 nm is 6.31 x [tex]10^14 Hz.[/tex]

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The volume of the vegetable oil is  0.00003998 m³.

The density of vegetable oil,

ρ = 913 kg/m³

The mass of vegetable oil,

m = 0.0365 kg

To find: The volume of the vegetable oil, V Solution: The density of any substance is defined as the mass of the substance per unit volume.

The formula for density is:

ρ = m/V

where, ρ is the density of the substancem is the mass of the substance V is the volume of the substance We can rearrange the above formula to find the volume of the substance:

V = m/ρSubstituting the given values of mass and density in the above formula,

We get:

V = 0.0365 kg / 913 kg/m³ = 0.00003998 m³ (approx)

Therefore, the volume of the vegetable oil is approximately 0.00003998 m³.

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