Question

"The density of material at the center of a neutron star is approximately 1.00 × 1018 kg/m3. What is the mass of a cube of this material that is 1.76 microns on each side. (One micron is equal to 1.00 × 10-6 m.)"

Answer 1

Q: "The density of material at the center of a neutron star is approximately 1.00 × 10¹⁸ kg/m3. What is the mass of a cube of this material that is 1.76 microns on each side. (One micron is equal to 1.00 × 10-6 m.)"

Answer:

5.452 kg

Explanation:

Density: This can be defined as the ratio of the mass of a substance to its volume. The S.I unit of density is kg/m³.

Mathematically, Density can be represented as

D = M/V

M = D×V ............................ Equation 1

Where D = density of the material, M = mass of the material, V = volume of the cube of the material,

But

V = L³

Where L = Length of the cube.

If 1 micron = 1.00×10⁻⁶ m,

Then, 1.76 microns = 1.76×10⁻⁶ m

Therefore L =  1.76×10⁻⁶ m

V =  (1.76×10⁻⁶ )³

V = 5.452×10⁻¹⁸ m³

Given: D = 1.0×10¹⁸ kg/m³,  and V = 5.452×10⁻¹⁸ m³

Substitute into equation 1

M = 1.0×10¹⁸×5.452×10⁻¹⁸

M =5.452 kg.

Hence the mass of the cube material = 5.452 kg