calculate the mass in kilograms of a small piece of a neutron star the size of a spherical pebble with a radius of 0.10 mm.
0.10 mm=0.010cm
V=(4/3)(0.010cm)^3=
M= (
i got this far now I am lost please help
To calculate the mass of the small piece of a neutron star, we need to use the equation for the volume of a sphere:
V = (4/3)πr³
where V represents the volume and r is the radius of the sphere. In this case, the radius is given as 0.010 cm.
First, substitute the value of the radius into the equation:
V = (4/3)π(0.010 cm)³
Now, we can calculate the volume of the small piece of the neutron star by simplifying the equation:
V = (4/3)π(0.01 cm)³
≈ (4/3)π(0.000001 cm³)
≈ (4/3) × 3.14159... × 0.000001 cm³
≈ 0.00000000418878 cm³
Now, let's convert the volume from cubic centimeters (cm³) to cubic meters (m³) by multiplying by the conversion factor:
1 cm³ = 0.000000001 m³
V = 0.00000000418878 cm³ × 0.000000001 m³/cm³
= 0.00000000000000418878 m³
The next step is to calculate the mass of the small piece of the neutron star using the density of a neutron star, which is approximately 10⁸ kg/m³. The formula for mass is:
M = ρV
where M represents the mass, ρ is the density, and V is the volume.
Substituting the values into the equation, we get:
M = (10⁸ kg/m³) × (0.00000000000000418878 m³)
= 0.000000000418878 kg
So, the mass of the small piece of the neutron star is approximately 0.000000000418878 kg.