The moon has radius 1740 km and mass 7.35x10^22? kg.What is its average density?

density ρ=m/V

V=4πR³/3
kilometers -> meters!

25353

To find the average density of the moon, we need to divide its mass by its volume.

Step 1: Calculate the volume of the moon.
The volume (V) of a sphere can be calculated using the formula:
V = (4/3) * π * (radius)^3

Substituting the given value, we have:
V = (4/3) * π * (1740 km)^3

Step 2: Convert the volume to cubic meters.
Since the density is commonly measured in kilograms per cubic meter, we need to convert the volume from cubic kilometers to cubic meters.
1 km = 1000 meters

So, V = (4/3) * π * (1740 km)^3 * (1000 meters)^3

Step 3: Calculate the mass divided by the volume.
The average density (ρ) can be calculated by dividing the mass by the volume.
ρ = mass / volume

Substituting the given values, we have:
ρ = 7.35 x 10^22 kg / V

Now we can go back to Step 2 and substitute the value of V we calculated.

Finally, we can calculate the average density of the moon.

To find the average density of the moon, you need to divide its mass by its volume. The formula for density is:

Density = Mass / Volume

First, let's calculate the volume of the moon. The formula for the volume of a sphere is:

Volume = (4/3) * π * radius^3

Substitute the given radius (1740 km) into the formula:

Volume = (4/3) * π * (1740 km)^3

Note that π is a constant value approximately equal to 3.14159.

Now, let's calculate the volume:

Volume = (4/3) * 3.14159 * (1740 km)^3

Next, convert the radius from kilometers to centimeters, since the mass is given in kg:

1 kilometer = 100,000 centimeters

So, the radius in centimeters is:

1740 km * 100,000 cm/km = 174,000,000 cm

Substitute this value into the volume formula:

Volume = (4/3) * 3.14159 * (174,000,000 cm)^3

After calculating the volume, you will have it in cubic centimeters (cm^3). Now, divide the mass of the moon (7.35x10^22 kg) by its volume to find the average density:

Density = Mass / Volume

Note that the mass is given in scientific notation. To perform the calculation, you can convert it to decimal form by moving the decimal point 22 places to the right:

7.35x10^22 kg = 735,000,000,000,000,000,000,000 kg

Substitute the mass and volume into the density formula:

Density = 735,000,000,000,000,000,000,000 kg / Volume

After performing the calculations, you will obtain the average density of the moon.